Bayesian regression
leechungpa
2021-05-31
1 Packages and Reference
We use BAS packages. We proceeded with reference to this example.
Also, I give my sincere gratitude to KKH.
library(BAS)
library(tidyverse)
library(plotly)2 Preprocessing
colnames(original_data)## [1] "X1" "idx" "population"
## [4] "householdsize" "racepctblack" "racePctWhite"
## [7] "racePctAsian" "racePctHisp" "agePct12t29"
## [10] "agePct65up" "numbUrban" "pctUrban"
## [13] "medIncome" "pctWWage" "pctWFarmSelf"
## [16] "pctWInvInc" "pctWSocSec" "pctWPubAsst"
## [19] "pctWRetire" "medFamInc" "whitePerCap"
## [22] "blackPerCap" "indianPerCap" "AsianPerCap"
## [25] "OtherPerCap" "HispPerCap" "NumUnderPov"
## [28] "PctPopUnderPov" "PctLess9thGrade" "PctBSorMore"
## [31] "PctUnemployed" "PctEmploy" "PctEmplManu"
## [34] "PctEmplProfServ" "PctOccupMgmtProf" "MalePctNevMarr"
## [37] "TotalPctDiv" "PersPerFam" "PctFam2Par"
## [40] "PctWorkMom" "PctKidsBornNeverMar" "NumImmig"
## [43] "PctImmigRecent" "PctRecentImmig" "PctSpeakEnglOnly"
## [46] "PctNotSpeakEnglWell" "PctLargHouseFam" "PersPerOccupHous"
## [49] "PersPerOwnOccHous" "PersPerRentOccHous" "PctPersOwnOccup"
## [52] "PctPersDenseHous" "PctHousLess3BR" "MedNumBR"
## [55] "HousVacant" "PctHousOccup" "PctHousOwnOcc"
## [58] "PctVacantBoarded" "PctVacMore6Mos" "MedYrHousBuilt"
## [61] "PctHousNoPhone" "PctWOFullPlumb" "OwnOccLowQuart"
## [64] "OwnOccMedVal" "OwnOccHiQuart" "RentLowQ"
## [67] "RentMedian" "RentHighQ" "MedRent"
## [70] "MedRentPctHousInc" "MedOwnCostPctInc" "MedOwnCostPctIncNoMtg"
## [73] "NumInShelters" "NumStreet" "PctForeignBorn"
## [76] "PctBornSameState" "PctSameHouse85" "PctSameCity85"
## [79] "PctSameState85" "LandArea" "PopDens"
## [82] "PctUsePubTrans" "LemasPctOfficDrugUn" "agePct22t29"
## [85] "murdPerPop" "rapesPerPop" "robbbPerPop"
## [88] "assaultPerPop" "burglPerPop" "larcPerPop"
## [91] "autoTheftPerPop" "arsonsPerPop"data = subset(original_data, select = -c(X1, idx))
data %>% head()## # A tibble: 6 x 90
## population householdsize racepctblack racePctWhite racePctAsian racePctHisp
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 -0.977 1.18 -0.559 0.475 0.856 -0.416
## 2 -0.214 0.337 -0.599 0.706 0.172 -0.487
## 3 0.0618 -0.830 -0.603 0.631 0.170 -0.384
## 4 -0.595 -0.920 -0.536 0.814 -0.485 -0.497
## 5 -1.05 0.158 -0.618 0.316 -0.335 -0.509
## 6 1.88 -0.770 -0.479 0.711 -0.396 -0.480
## # … with 84 more variables: agePct12t29 <dbl>, agePct65up <dbl>,
## # numbUrban <dbl>, pctUrban <dbl>, medIncome <dbl>, pctWWage <dbl>,
## # pctWFarmSelf <dbl>, pctWInvInc <dbl>, pctWSocSec <dbl>, pctWPubAsst <dbl>,
## # pctWRetire <dbl>, medFamInc <dbl>, whitePerCap <dbl>, blackPerCap <dbl>,
## # indianPerCap <dbl>, AsianPerCap <dbl>, OtherPerCap <dbl>, HispPerCap <dbl>,
## # NumUnderPov <dbl>, PctPopUnderPov <dbl>, PctLess9thGrade <dbl>,
## # PctBSorMore <dbl>, PctUnemployed <dbl>, PctEmploy <dbl>, PctEmplManu <dbl>,
## # PctEmplProfServ <dbl>, PctOccupMgmtProf <dbl>, MalePctNevMarr <dbl>,
## # TotalPctDiv <dbl>, PersPerFam <dbl>, PctFam2Par <dbl>, PctWorkMom <dbl>,
## # PctKidsBornNeverMar <dbl>, NumImmig <dbl>, PctImmigRecent <dbl>,
## # PctRecentImmig <dbl>, PctSpeakEnglOnly <dbl>, PctNotSpeakEnglWell <dbl>,
## # PctLargHouseFam <dbl>, PersPerOccupHous <dbl>, PersPerOwnOccHous <dbl>,
## # PersPerRentOccHous <dbl>, PctPersOwnOccup <dbl>, PctPersDenseHous <dbl>,
## # PctHousLess3BR <dbl>, MedNumBR <dbl>, HousVacant <dbl>, PctHousOccup <dbl>,
## # PctHousOwnOcc <dbl>, PctVacantBoarded <dbl>, PctVacMore6Mos <dbl>,
## # MedYrHousBuilt <dbl>, PctHousNoPhone <dbl>, PctWOFullPlumb <dbl>,
## # OwnOccLowQuart <dbl>, OwnOccMedVal <dbl>, OwnOccHiQuart <dbl>,
## # RentLowQ <dbl>, RentMedian <dbl>, RentHighQ <dbl>, MedRent <dbl>,
## # MedRentPctHousInc <dbl>, MedOwnCostPctInc <dbl>,
## # MedOwnCostPctIncNoMtg <dbl>, NumInShelters <dbl>, NumStreet <dbl>,
## # PctForeignBorn <dbl>, PctBornSameState <dbl>, PctSameHouse85 <dbl>,
## # PctSameCity85 <dbl>, PctSameState85 <dbl>, LandArea <dbl>, PopDens <dbl>,
## # PctUsePubTrans <dbl>, LemasPctOfficDrugUn <dbl>, agePct22t29 <dbl>,
## # murdPerPop <dbl>, rapesPerPop <dbl>, robbbPerPop <dbl>,
## # assaultPerPop <dbl>, burglPerPop <dbl>, larcPerPop <dbl>,
## # autoTheftPerPop <dbl>, arsonsPerPop <dbl>3 murdPerPop
y_name = 'murdPerPop'3.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
3.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.0000 1.00000000 1.000000e+00
## population 0.72241 1.0000 0.00000000 0.000000e+00
## householdsize 0.09946 0.0000 0.00000000 0.000000e+00
## racepctblack 0.98390 1.0000 1.00000000 1.000000e+00
## racePctWhite 0.70205 0.0000 1.00000000 0.000000e+00
## racePctAsian 0.10683 0.0000 0.00000000 0.000000e+00
## racePctHisp 0.10775 0.0000 0.00000000 0.000000e+00
## agePct12t29 0.33904 1.0000 0.00000000 0.000000e+00
## agePct65up 0.11923 0.0000 0.00000000 0.000000e+00
## numbUrban 0.08325 0.0000 0.00000000 0.000000e+00
## pctUrban 0.08891 0.0000 0.00000000 0.000000e+00
## medIncome 0.11219 0.0000 0.00000000 0.000000e+00
## pctWWage 0.37848 0.0000 0.00000000 0.000000e+00
## pctWFarmSelf 0.07752 0.0000 0.00000000 0.000000e+00
## pctWInvInc 0.09398 0.0000 0.00000000 0.000000e+00
## pctWSocSec 0.17205 0.0000 0.00000000 0.000000e+00
## pctWPubAsst 0.09952 0.0000 0.00000000 0.000000e+00
## pctWRetire 0.33569 0.0000 0.00000000 1.000000e+00
## medFamInc 0.40717 0.0000 1.00000000 0.000000e+00
## whitePerCap 0.43736 0.0000 1.00000000 0.000000e+00
## blackPerCap 0.06729 0.0000 0.00000000 0.000000e+00
## indianPerCap 0.07136 0.0000 0.00000000 0.000000e+00
## AsianPerCap 0.07313 0.0000 0.00000000 0.000000e+00
## OtherPerCap 0.06845 0.0000 0.00000000 0.000000e+00
## HispPerCap 0.08464 0.0000 0.00000000 0.000000e+00
## NumUnderPov 0.63998 1.0000 0.00000000 0.000000e+00
## PctPopUnderPov 0.32094 0.0000 0.00000000 0.000000e+00
## PctLess9thGrade 0.10595 0.0000 0.00000000 1.000000e+00
## PctBSorMore 0.08597 0.0000 0.00000000 0.000000e+00
## PctUnemployed 0.16859 0.0000 0.00000000 0.000000e+00
## PctEmploy 0.25523 0.0000 0.00000000 0.000000e+00
## PctEmplManu 0.44242 0.0000 1.00000000 1.000000e+00
## PctEmplProfServ 0.09205 0.0000 0.00000000 0.000000e+00
## PctOccupMgmtProf 0.09580 0.0000 0.00000000 0.000000e+00
## MalePctNevMarr 0.16312 0.0000 0.00000000 0.000000e+00
## TotalPctDiv 0.17850 0.0000 0.00000000 0.000000e+00
## PersPerFam 0.32913 1.0000 0.00000000 0.000000e+00
## PctFam2Par 0.85712 1.0000 1.00000000 1.000000e+00
## PctWorkMom 0.93975 1.0000 1.00000000 1.000000e+00
## PctKidsBornNeverMar 0.12638 0.0000 0.00000000 0.000000e+00
## NumImmig 0.10957 0.0000 0.00000000 0.000000e+00
## PctImmigRecent 0.07149 0.0000 0.00000000 0.000000e+00
## PctRecentImmig 0.11983 0.0000 0.00000000 0.000000e+00
## PctSpeakEnglOnly 0.84790 1.0000 1.00000000 0.000000e+00
## PctNotSpeakEnglWell 0.46304 0.0000 0.00000000 0.000000e+00
## PctLargHouseFam 0.13795 0.0000 0.00000000 1.000000e+00
## PersPerOccupHous 0.17992 0.0000 0.00000000 0.000000e+00
## PersPerOwnOccHous 0.63062 1.0000 0.00000000 1.000000e+00
## PersPerRentOccHous 0.12389 0.0000 0.00000000 0.000000e+00
## PctPersOwnOccup 0.18349 0.0000 0.00000000 1.000000e+00
## PctPersDenseHous 0.91608 1.0000 1.00000000 1.000000e+00
## PctHousLess3BR 0.15205 0.0000 0.00000000 0.000000e+00
## MedNumBR 0.14372 0.0000 0.00000000 0.000000e+00
## HousVacant 0.59136 0.0000 1.00000000 0.000000e+00
## PctHousOccup 0.12012 0.0000 0.00000000 0.000000e+00
## PctHousOwnOcc 0.27723 0.0000 0.00000000 0.000000e+00
## PctVacantBoarded 0.99963 1.0000 1.00000000 1.000000e+00
## PctVacMore6Mos 0.25100 0.0000 0.00000000 1.000000e+00
## MedYrHousBuilt 0.20321 0.0000 0.00000000 0.000000e+00
## PctHousNoPhone 0.07940 0.0000 0.00000000 0.000000e+00
## PctWOFullPlumb 0.88715 1.0000 1.00000000 1.000000e+00
## OwnOccLowQuart 0.11106 0.0000 0.00000000 0.000000e+00
## OwnOccMedVal 0.10642 0.0000 0.00000000 0.000000e+00
## OwnOccHiQuart 0.11107 0.0000 0.00000000 0.000000e+00
## RentLowQ 0.08455 0.0000 0.00000000 0.000000e+00
## RentMedian 0.09244 0.0000 0.00000000 1.000000e+00
## RentHighQ 0.10569 0.0000 0.00000000 0.000000e+00
## MedRent 0.11882 0.0000 1.00000000 0.000000e+00
## MedRentPctHousInc 0.18653 0.0000 0.00000000 0.000000e+00
## MedOwnCostPctInc 0.08294 0.0000 0.00000000 0.000000e+00
## MedOwnCostPctIncNoMtg 0.06575 0.0000 0.00000000 0.000000e+00
## NumInShelters 0.16761 0.0000 0.00000000 0.000000e+00
## NumStreet 0.76426 1.0000 1.00000000 1.000000e+00
## PctForeignBorn 0.14487 0.0000 0.00000000 0.000000e+00
## PctBornSameState 0.11327 0.0000 0.00000000 0.000000e+00
## PctSameHouse85 0.12127 0.0000 0.00000000 1.000000e+00
## PctSameCity85 0.08401 0.0000 0.00000000 0.000000e+00
## PctSameState85 0.08189 0.0000 1.00000000 0.000000e+00
## LandArea 0.81535 1.0000 1.00000000 1.000000e+00
## PopDens 0.26511 0.0000 0.00000000 0.000000e+00
## PctUsePubTrans 0.28357 0.0000 0.00000000 0.000000e+00
## LemasPctOfficDrugUn 0.06621 0.0000 0.00000000 0.000000e+00
## agePct22t29 0.13927 0.0000 0.00000000 0.000000e+00
## BF NA 1.0000 0.01090494 8.797887e-06
## PostProbs NA 0.0009 0.00050000 5.000000e-04
## R2 NA 0.5793 0.57980000 5.779000e-01
## dim NA 15.0000 17.00000000 1.800000e+01
## logmarg NA 775.2954 770.77690577 7.636544e+02
## model 4 model 5
## Intercept 1.00000000 1.00000000
## population 1.00000000 1.00000000
## householdsize 0.00000000 0.00000000
## racepctblack 1.00000000 1.00000000
## racePctWhite 0.00000000 1.00000000
## racePctAsian 0.00000000 0.00000000
## racePctHisp 0.00000000 0.00000000
## agePct12t29 0.00000000 0.00000000
## agePct65up 0.00000000 0.00000000
## numbUrban 0.00000000 0.00000000
## pctUrban 0.00000000 0.00000000
## medIncome 1.00000000 0.00000000
## pctWWage 0.00000000 1.00000000
## pctWFarmSelf 0.00000000 0.00000000
## pctWInvInc 0.00000000 0.00000000
## pctWSocSec 0.00000000 0.00000000
## pctWPubAsst 0.00000000 0.00000000
## pctWRetire 0.00000000 1.00000000
## medFamInc 1.00000000 0.00000000
## whitePerCap 1.00000000 0.00000000
## blackPerCap 0.00000000 0.00000000
## indianPerCap 0.00000000 0.00000000
## AsianPerCap 0.00000000 0.00000000
## OtherPerCap 0.00000000 0.00000000
## HispPerCap 0.00000000 0.00000000
## NumUnderPov 1.00000000 1.00000000
## PctPopUnderPov 0.00000000 0.00000000
## PctLess9thGrade 0.00000000 0.00000000
## PctBSorMore 0.00000000 0.00000000
## PctUnemployed 0.00000000 0.00000000
## PctEmploy 0.00000000 0.00000000
## PctEmplManu 0.00000000 0.00000000
## PctEmplProfServ 0.00000000 1.00000000
## PctOccupMgmtProf 0.00000000 0.00000000
## MalePctNevMarr 0.00000000 0.00000000
## TotalPctDiv 0.00000000 0.00000000
## PersPerFam 0.00000000 1.00000000
## PctFam2Par 1.00000000 1.00000000
## PctWorkMom 1.00000000 1.00000000
## PctKidsBornNeverMar 0.00000000 0.00000000
## NumImmig 0.00000000 0.00000000
## PctImmigRecent 0.00000000 0.00000000
## PctRecentImmig 0.00000000 0.00000000
## PctSpeakEnglOnly 1.00000000 1.00000000
## PctNotSpeakEnglWell 0.00000000 0.00000000
## PctLargHouseFam 0.00000000 0.00000000
## PersPerOccupHous 0.00000000 0.00000000
## PersPerOwnOccHous 0.00000000 1.00000000
## PersPerRentOccHous 0.00000000 0.00000000
## PctPersOwnOccup 0.00000000 0.00000000
## PctPersDenseHous 1.00000000 1.00000000
## PctHousLess3BR 0.00000000 0.00000000
## MedNumBR 0.00000000 0.00000000
## HousVacant 0.00000000 0.00000000
## PctHousOccup 0.00000000 0.00000000
## PctHousOwnOcc 1.00000000 0.00000000
## PctVacantBoarded 1.00000000 1.00000000
## PctVacMore6Mos 0.00000000 0.00000000
## MedYrHousBuilt 0.00000000 0.00000000
## PctHousNoPhone 0.00000000 0.00000000
## PctWOFullPlumb 1.00000000 1.00000000
## OwnOccLowQuart 0.00000000 0.00000000
## OwnOccMedVal 0.00000000 0.00000000
## OwnOccHiQuart 0.00000000 0.00000000
## RentLowQ 0.00000000 0.00000000
## RentMedian 0.00000000 0.00000000
## RentHighQ 0.00000000 0.00000000
## MedRent 0.00000000 0.00000000
## MedRentPctHousInc 0.00000000 0.00000000
## MedOwnCostPctInc 0.00000000 0.00000000
## MedOwnCostPctIncNoMtg 0.00000000 0.00000000
## NumInShelters 0.00000000 0.00000000
## NumStreet 1.00000000 1.00000000
## PctForeignBorn 0.00000000 0.00000000
## PctBornSameState 0.00000000 0.00000000
## PctSameHouse85 0.00000000 0.00000000
## PctSameCity85 0.00000000 0.00000000
## PctSameState85 0.00000000 0.00000000
## LandArea 1.00000000 1.00000000
## PopDens 0.00000000 0.00000000
## PctUsePubTrans 0.00000000 0.00000000
## LemasPctOfficDrugUn 0.00000000 0.00000000
## agePct22t29 0.00000000 0.00000000
## BF 0.01629809 0.06800977
## PostProbs 0.00050000 0.00040000
## R2 0.57870000 0.58190000
## dim 16.00000000 18.00000000
## logmarg 771.17873775 772.60734105top 5 model
3.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
3.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 23979 models
## post mean post SD post p(B != 0)
## Intercept 5.968e+00 1.353e-01 1.000e+00
## population 1.546e+00 1.257e+00 7.224e-01
## householdsize -3.540e-03 1.467e-01 9.946e-02
## racepctblack 2.454e+00 8.287e-01 9.839e-01
## racePctWhite -1.130e+00 9.408e-01 7.020e-01
## racePctAsian -2.100e-02 1.276e-01 1.068e-01
## racePctHisp -3.052e-02 2.288e-01 1.077e-01
## agePct12t29 -2.317e-01 4.176e-01 3.390e-01
## agePct65up -3.539e-02 2.279e-01 1.192e-01
## numbUrban 1.152e-02 1.113e-01 8.325e-02
## pctUrban 3.569e-03 1.026e-01 8.891e-02
## medIncome -1.645e-02 4.682e-01 1.122e-01
## pctWWage -4.788e-01 7.663e-01 3.785e-01
## pctWFarmSelf 5.406e-03 5.384e-02 7.752e-02
## pctWInvInc -2.073e-02 1.591e-01 9.398e-02
## pctWSocSec -1.527e-01 4.560e-01 1.721e-01
## pctWPubAsst 3.175e-02 1.671e-01 9.952e-02
## pctWRetire -1.511e-01 2.521e-01 3.357e-01
## medFamInc -8.236e-01 1.218e+00 4.072e-01
## whitePerCap 6.038e-01 8.264e-01 4.374e-01
## blackPerCap 1.715e-06 4.309e-02 6.729e-02
## indianPerCap 1.371e-03 3.617e-02 7.136e-02
## AsianPerCap 3.780e-03 4.543e-02 7.313e-02
## OtherPerCap 6.224e-03 4.445e-02 6.845e-02
## HispPerCap 9.400e-03 6.398e-02 8.464e-02
## NumUnderPov -1.503e+00 1.420e+00 6.400e-01
## PctPopUnderPov 3.609e-01 6.536e-01 3.209e-01
## PctLess9thGrade -3.459e-02 1.622e-01 1.060e-01
## PctBSorMore -1.470e-02 1.285e-01 8.597e-02
## PctUnemployed -7.284e-02 2.115e-01 1.686e-01
## PctEmploy 2.121e-01 4.525e-01 2.552e-01
## PctEmplManu 1.730e-01 2.297e-01 4.424e-01
## PctEmplProfServ -1.928e-04 7.324e-02 9.205e-02
## PctOccupMgmtProf 8.597e-03 1.254e-01 9.580e-02
## MalePctNevMarr 8.435e-02 3.059e-01 1.631e-01
## TotalPctDiv 8.672e-02 2.587e-01 1.785e-01
## PersPerFam 4.240e-01 7.433e-01 3.291e-01
## PctFam2Par -1.371e+00 7.383e-01 8.571e-01
## PctWorkMom -6.935e-01 2.707e-01 9.397e-01
## PctKidsBornNeverMar 5.712e-02 2.532e-01 1.264e-01
## NumImmig -3.712e-02 2.333e-01 1.096e-01
## PctImmigRecent -2.873e-03 5.037e-02 7.149e-02
## PctRecentImmig 4.122e-02 1.893e-01 1.198e-01
## PctSpeakEnglOnly 1.235e+00 7.657e-01 8.479e-01
## PctNotSpeakEnglWell 6.086e-01 7.891e-01 4.630e-01
## PctLargHouseFam 6.210e-02 2.675e-01 1.379e-01
## PersPerOccupHous 1.841e-01 6.239e-01 1.799e-01
## PersPerOwnOccHous -8.745e-01 8.588e-01 6.306e-01
## PersPerRentOccHous -2.310e-02 2.348e-01 1.239e-01
## PctPersOwnOccup -1.532e-01 9.191e-01 1.835e-01
## PctPersDenseHous 1.798e+00 7.949e-01 9.161e-01
## PctHousLess3BR 7.144e-02 2.454e-01 1.520e-01
## MedNumBR -3.795e-02 1.211e-01 1.437e-01
## HousVacant 2.908e-01 2.874e-01 5.914e-01
## PctHousOccup -2.391e-02 9.686e-02 1.201e-01
## PctHousOwnOcc 3.618e-01 9.716e-01 2.772e-01
## PctVacantBoarded 1.662e+00 2.014e-01 9.996e-01
## PctVacMore6Mos -8.467e-02 1.794e-01 2.510e-01
## MedYrHousBuilt -7.134e-02 1.814e-01 2.032e-01
## PctHousNoPhone 1.702e-02 1.090e-01 7.940e-02
## PctWOFullPlumb -5.132e-01 2.528e-01 8.871e-01
## OwnOccLowQuart -3.963e-02 1.952e-01 1.111e-01
## OwnOccMedVal -2.816e-02 2.004e-01 1.064e-01
## OwnOccHiQuart -3.980e-02 1.862e-01 1.111e-01
## RentLowQ -2.464e-04 1.249e-01 8.455e-02
## RentMedian -2.468e-02 2.899e-01 9.244e-02
## RentHighQ 3.896e-02 2.197e-01 1.057e-01
## MedRent 6.705e-02 3.212e-01 1.188e-01
## MedRentPctHousInc 6.054e-02 1.602e-01 1.865e-01
## MedOwnCostPctInc -6.613e-03 7.213e-02 8.294e-02
## MedOwnCostPctIncNoMtg 3.758e-03 4.882e-02 6.575e-02
## NumInShelters 5.152e-02 1.465e-01 1.676e-01
## NumStreet 4.202e-01 2.913e-01 7.643e-01
## PctForeignBorn -9.897e-02 3.406e-01 1.449e-01
## PctBornSameState 2.618e-02 1.050e-01 1.133e-01
## PctSameHouse85 3.637e-02 1.493e-01 1.213e-01
## PctSameCity85 7.299e-03 8.567e-02 8.401e-02
## PctSameState85 8.782e-03 7.263e-02 8.189e-02
## LandArea 6.961e-01 4.091e-01 8.154e-01
## PopDens -1.461e-01 3.001e-01 2.651e-01
## PctUsePubTrans 1.157e-01 2.237e-01 2.836e-01
## LemasPctOfficDrugUn 4.894e-04 4.276e-02 6.621e-02
## agePct22t29 -3.561e-02 1.429e-01 1.393e-013.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
3.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL3.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)4 rapesPerPop
y_name = 'rapesPerPop'4.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
4.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3 model 4
## Intercept 1.00000 1.000000 1.000000 1.000000e+00 1.0000
## population 0.17079 0.000000 0.000000 0.000000e+00 1.0000
## householdsize 0.12428 0.000000 0.000000 0.000000e+00 0.0000
## racepctblack 0.18891 0.000000 0.000000 0.000000e+00 1.0000
## racePctWhite 0.47841 0.000000 0.000000 1.000000e+00 0.0000
## racePctAsian 0.11505 0.000000 0.000000 0.000000e+00 0.0000
## racePctHisp 0.73507 1.000000 1.000000 0.000000e+00 1.0000
## agePct12t29 0.35788 0.000000 0.000000 1.000000e+00 0.0000
## agePct65up 0.15857 0.000000 0.000000 0.000000e+00 0.0000
## numbUrban 0.11212 0.000000 0.000000 0.000000e+00 0.0000
## pctUrban 0.14196 0.000000 0.000000 0.000000e+00 0.0000
## medIncome 0.36661 0.000000 0.000000 1.000000e+00 1.0000
## pctWWage 0.16627 0.000000 0.000000 0.000000e+00 0.0000
## pctWFarmSelf 0.25505 0.000000 0.000000 0.000000e+00 0.0000
## pctWInvInc 0.16440 0.000000 0.000000 0.000000e+00 0.0000
## pctWSocSec 0.30785 0.000000 1.000000 1.000000e+00 1.0000
## pctWPubAsst 0.17971 0.000000 0.000000 0.000000e+00 0.0000
## pctWRetire 0.09631 0.000000 0.000000 1.000000e+00 0.0000
## medFamInc 0.19363 0.000000 0.000000 0.000000e+00 0.0000
## whitePerCap 0.13679 0.000000 1.000000 1.000000e+00 0.0000
## blackPerCap 0.17823 0.000000 0.000000 0.000000e+00 0.0000
## indianPerCap 0.08147 1.000000 0.000000 0.000000e+00 0.0000
## AsianPerCap 0.09725 0.000000 0.000000 0.000000e+00 0.0000
## OtherPerCap 0.68301 1.000000 0.000000 1.000000e+00 1.0000
## HispPerCap 0.17658 0.000000 1.000000 0.000000e+00 0.0000
## NumUnderPov 0.13854 0.000000 0.000000 0.000000e+00 0.0000
## PctPopUnderPov 0.15234 0.000000 0.000000 1.000000e+00 1.0000
## PctLess9thGrade 0.99785 1.000000 1.000000 1.000000e+00 1.0000
## PctBSorMore 0.17624 0.000000 0.000000 0.000000e+00 0.0000
## PctUnemployed 0.66368 1.000000 1.000000 0.000000e+00 1.0000
## PctEmploy 0.19160 1.000000 0.000000 0.000000e+00 0.0000
## PctEmplManu 0.12737 0.000000 0.000000 0.000000e+00 0.0000
## PctEmplProfServ 0.09685 0.000000 0.000000 0.000000e+00 0.0000
## PctOccupMgmtProf 0.28694 0.000000 0.000000 0.000000e+00 0.0000
## MalePctNevMarr 0.12311 0.000000 0.000000 0.000000e+00 0.0000
## TotalPctDiv 0.99988 1.000000 1.000000 1.000000e+00 1.0000
## PersPerFam 0.29158 1.000000 1.000000 0.000000e+00 0.0000
## PctFam2Par 0.11799 0.000000 0.000000 0.000000e+00 0.0000
## PctWorkMom 0.19785 0.000000 0.000000 0.000000e+00 0.0000
## PctKidsBornNeverMar 0.55149 1.000000 1.000000 0.000000e+00 0.0000
## NumImmig 0.13625 0.000000 0.000000 0.000000e+00 0.0000
## PctImmigRecent 0.15171 0.000000 0.000000 0.000000e+00 0.0000
## PctRecentImmig 0.12426 0.000000 0.000000 0.000000e+00 0.0000
## PctSpeakEnglOnly 0.25162 0.000000 0.000000 1.000000e+00 0.0000
## PctNotSpeakEnglWell 0.09658 0.000000 0.000000 0.000000e+00 0.0000
## PctLargHouseFam 0.36884 0.000000 0.000000 1.000000e+00 1.0000
## PersPerOccupHous 0.27671 0.000000 0.000000 0.000000e+00 0.0000
## PersPerOwnOccHous 0.12975 0.000000 0.000000 0.000000e+00 0.0000
## PersPerRentOccHous 0.12179 1.000000 0.000000 0.000000e+00 0.0000
## PctPersOwnOccup 0.73021 1.000000 1.000000 0.000000e+00 1.0000
## PctPersDenseHous 0.19380 0.000000 0.000000 0.000000e+00 0.0000
## PctHousLess3BR 0.11005 0.000000 0.000000 0.000000e+00 0.0000
## MedNumBR 0.27777 0.000000 0.000000 0.000000e+00 0.0000
## HousVacant 0.11109 0.000000 0.000000 1.000000e+00 0.0000
## PctHousOccup 0.43095 0.000000 0.000000 1.000000e+00 0.0000
## PctHousOwnOcc 0.31881 0.000000 0.000000 1.000000e+00 0.0000
## PctVacantBoarded 0.79879 1.000000 1.000000 1.000000e+00 1.0000
## PctVacMore6Mos 0.08111 0.000000 0.000000 0.000000e+00 0.0000
## MedYrHousBuilt 0.31784 0.000000 0.000000 0.000000e+00 0.0000
## PctHousNoPhone 0.99731 1.000000 1.000000 1.000000e+00 1.0000
## PctWOFullPlumb 0.17700 0.000000 0.000000 0.000000e+00 0.0000
## OwnOccLowQuart 0.18149 1.000000 0.000000 1.000000e+00 0.0000
## OwnOccMedVal 0.27885 0.000000 0.000000 0.000000e+00 0.0000
## OwnOccHiQuart 0.60947 0.000000 0.000000 0.000000e+00 1.0000
## RentLowQ 0.18757 0.000000 0.000000 0.000000e+00 0.0000
## RentMedian 0.27169 0.000000 0.000000 0.000000e+00 0.0000
## RentHighQ 0.10597 0.000000 0.000000 0.000000e+00 0.0000
## MedRent 0.18519 0.000000 0.000000 0.000000e+00 0.0000
## MedRentPctHousInc 0.17910 0.000000 0.000000 0.000000e+00 0.0000
## MedOwnCostPctInc 0.21503 0.000000 1.000000 0.000000e+00 0.0000
## MedOwnCostPctIncNoMtg 0.17921 0.000000 0.000000 0.000000e+00 0.0000
## NumInShelters 0.48236 1.000000 0.000000 0.000000e+00 0.0000
## NumStreet 0.97218 1.000000 1.000000 1.000000e+00 1.0000
## PctForeignBorn 0.11832 0.000000 0.000000 0.000000e+00 0.0000
## PctBornSameState 0.70002 1.000000 1.000000 1.000000e+00 0.0000
## PctSameHouse85 0.10566 0.000000 0.000000 0.000000e+00 0.0000
## PctSameCity85 0.62188 1.000000 0.000000 1.000000e+00 0.0000
## PctSameState85 0.15228 0.000000 1.000000 0.000000e+00 0.0000
## LandArea 0.58143 0.000000 1.000000 1.000000e+00 1.0000
## PopDens 0.87260 1.000000 1.000000 1.000000e+00 0.0000
## PctUsePubTrans 0.11863 0.000000 0.000000 0.000000e+00 0.0000
## LemasPctOfficDrugUn 0.08537 0.000000 0.000000 0.000000e+00 0.0000
## agePct22t29 0.10488 0.000000 0.000000 0.000000e+00 0.0000
## BF NA 0.120061 0.877204 6.091676e-04 1.0000
## PostProbs NA 0.000400 0.000400 4.000000e-04 0.0003
## R2 NA 0.436900 0.436500 4.398000e-01 0.4350
## dim NA 20.000000 19.000000 2.400000e+01 18.0000
## logmarg NA 487.096306 489.085046 4.818126e+02 489.2161
## model 5
## Intercept 1.000000e+00
## population 0.000000e+00
## householdsize 0.000000e+00
## racepctblack 0.000000e+00
## racePctWhite 0.000000e+00
## racePctAsian 0.000000e+00
## racePctHisp 1.000000e+00
## agePct12t29 1.000000e+00
## agePct65up 0.000000e+00
## numbUrban 0.000000e+00
## pctUrban 0.000000e+00
## medIncome 1.000000e+00
## pctWWage 0.000000e+00
## pctWFarmSelf 0.000000e+00
## pctWInvInc 0.000000e+00
## pctWSocSec 1.000000e+00
## pctWPubAsst 0.000000e+00
## pctWRetire 0.000000e+00
## medFamInc 0.000000e+00
## whitePerCap 0.000000e+00
## blackPerCap 0.000000e+00
## indianPerCap 1.000000e+00
## AsianPerCap 0.000000e+00
## OtherPerCap 1.000000e+00
## HispPerCap 0.000000e+00
## NumUnderPov 0.000000e+00
## PctPopUnderPov 0.000000e+00
## PctLess9thGrade 1.000000e+00
## PctBSorMore 1.000000e+00
## PctUnemployed 1.000000e+00
## PctEmploy 0.000000e+00
## PctEmplManu 0.000000e+00
## PctEmplProfServ 0.000000e+00
## PctOccupMgmtProf 0.000000e+00
## MalePctNevMarr 0.000000e+00
## TotalPctDiv 1.000000e+00
## PersPerFam 1.000000e+00
## PctFam2Par 0.000000e+00
## PctWorkMom 0.000000e+00
## PctKidsBornNeverMar 1.000000e+00
## NumImmig 0.000000e+00
## PctImmigRecent 0.000000e+00
## PctRecentImmig 0.000000e+00
## PctSpeakEnglOnly 0.000000e+00
## PctNotSpeakEnglWell 0.000000e+00
## PctLargHouseFam 0.000000e+00
## PersPerOccupHous 0.000000e+00
## PersPerOwnOccHous 0.000000e+00
## PersPerRentOccHous 0.000000e+00
## PctPersOwnOccup 1.000000e+00
## PctPersDenseHous 0.000000e+00
## PctHousLess3BR 0.000000e+00
## MedNumBR 0.000000e+00
## HousVacant 0.000000e+00
## PctHousOccup 1.000000e+00
## PctHousOwnOcc 0.000000e+00
## PctVacantBoarded 0.000000e+00
## PctVacMore6Mos 0.000000e+00
## MedYrHousBuilt 0.000000e+00
## PctHousNoPhone 1.000000e+00
## PctWOFullPlumb 0.000000e+00
## OwnOccLowQuart 0.000000e+00
## OwnOccMedVal 1.000000e+00
## OwnOccHiQuart 0.000000e+00
## RentLowQ 0.000000e+00
## RentMedian 0.000000e+00
## RentHighQ 0.000000e+00
## MedRent 0.000000e+00
## MedRentPctHousInc 1.000000e+00
## MedOwnCostPctInc 1.000000e+00
## MedOwnCostPctIncNoMtg 0.000000e+00
## NumInShelters 0.000000e+00
## NumStreet 1.000000e+00
## PctForeignBorn 0.000000e+00
## PctBornSameState 0.000000e+00
## PctSameHouse85 0.000000e+00
## PctSameCity85 0.000000e+00
## PctSameState85 0.000000e+00
## LandArea 1.000000e+00
## PopDens 1.000000e+00
## PctUsePubTrans 0.000000e+00
## LemasPctOfficDrugUn 0.000000e+00
## agePct22t29 0.000000e+00
## BF 4.979803e-03
## PostProbs 3.000000e-04
## R2 4.381000e-01
## dim 2.200000e+01
## logmarg 4.839137e+02top 5 model
4.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
4.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 28776 models
## post mean post SD post p(B != 0)
## Intercept 36.25610 0.59412 1.00000
## population -0.11276 1.01018 0.17079
## householdsize -0.11151 0.93677 0.12428
## racepctblack 0.29775 1.21553 0.18891
## racePctWhite -1.59671 2.02059 0.47841
## racePctAsian -0.07236 0.47004 0.11505
## racePctHisp -3.02083 2.24939 0.73507
## agePct12t29 1.13897 1.87971 0.35788
## agePct65up 0.19464 1.16251 0.15857
## numbUrban -0.01751 1.00458 0.11212
## pctUrban 0.22773 1.05728 0.14196
## medIncome 2.21848 3.65338 0.36661
## pctWWage -0.34731 1.26791 0.16627
## pctWFarmSelf 0.30822 0.64516 0.25505
## pctWInvInc 0.40781 1.27863 0.16440
## pctWSocSec 1.00213 1.90600 0.30785
## pctWPubAsst 0.40263 1.14316 0.17971
## pctWRetire 0.02619 0.35150 0.09631
## medFamInc 0.50790 2.33743 0.19363
## whitePerCap -0.29561 1.21273 0.13679
## blackPerCap -0.17034 0.47447 0.17823
## indianPerCap -0.03105 0.19822 0.08147
## AsianPerCap -0.04269 0.25657 0.09725
## OtherPerCap 1.10085 0.91810 0.68301
## HispPerCap 0.21328 0.59536 0.17658
## NumUnderPov 0.05197 0.96951 0.13854
## PctPopUnderPov 0.31834 1.26037 0.15234
## PctLess9thGrade -6.69376 1.62698 0.99785
## PctBSorMore -0.37315 1.17923 0.17624
## PctUnemployed 2.29983 1.96959 0.66368
## PctEmploy -0.34463 1.11792 0.19160
## PctEmplManu -0.09810 0.40049 0.12737
## PctEmplProfServ -0.02371 0.40108 0.09685
## PctOccupMgmtProf -0.74581 1.48715 0.28694
## MalePctNevMarr 0.09771 0.73528 0.12311
## TotalPctDiv 8.19613 1.81851 0.99988
## PersPerFam 0.98149 2.06481 0.29158
## PctFam2Par -0.06169 1.29843 0.11799
## PctWorkMom -0.24254 0.63565 0.19785
## PctKidsBornNeverMar 2.15794 2.30047 0.55149
## NumImmig 0.15681 0.85698 0.13625
## PctImmigRecent -0.13489 0.43956 0.15171
## PctRecentImmig -0.14374 0.65267 0.12426
## PctSpeakEnglOnly 0.86073 1.90558 0.25162
## PctNotSpeakEnglWell -0.03239 0.83834 0.09658
## PctLargHouseFam 1.21245 1.88684 0.36884
## PersPerOccupHous 1.14790 2.47340 0.27671
## PersPerOwnOccHous 0.18351 1.14294 0.12975
## PersPerRentOccHous 0.02096 0.76441 0.12179
## PctPersOwnOccup -5.25998 4.40554 0.73021
## PctPersDenseHous 0.55119 1.52723 0.19380
## PctHousLess3BR 0.10468 0.67733 0.11005
## MedNumBR -0.42230 0.82596 0.27777
## HousVacant -0.08871 0.39142 0.11109
## PctHousOccup -0.69056 0.95427 0.43095
## PctHousOwnOcc -1.08059 3.75318 0.31881
## PctVacantBoarded 1.91334 1.24028 0.79879
## PctVacMore6Mos -0.02101 0.27477 0.08111
## MedYrHousBuilt -0.63393 1.13524 0.31784
## PctHousNoPhone 5.89062 1.41743 0.99731
## PctWOFullPlumb 0.17295 0.50240 0.17700
## OwnOccLowQuart -0.33960 1.86634 0.18149
## OwnOccMedVal -1.15216 2.64063 0.27885
## OwnOccHiQuart -3.13778 2.98783 0.60947
## RentLowQ -0.63935 1.88790 0.18757
## RentMedian 2.09413 4.70180 0.27169
## RentHighQ 0.05232 1.03815 0.10597
## MedRent -0.92039 3.17173 0.18519
## MedRentPctHousInc 0.24519 0.66782 0.17910
## MedOwnCostPctInc -0.36641 0.88885 0.21503
## MedOwnCostPctIncNoMtg -0.19282 0.53333 0.17921
## NumInShelters 0.93103 1.16441 0.48236
## NumStreet 2.99064 1.01206 0.97218
## PctForeignBorn -0.04504 0.81967 0.11832
## PctBornSameState -1.99765 1.64692 0.70002
## PctSameHouse85 0.07853 0.63592 0.10566
## PctSameCity85 2.04101 1.92290 0.62188
## PctSameState85 0.09983 0.75832 0.15228
## LandArea 1.53476 1.62351 0.58143
## PopDens -3.02078 1.57802 0.87260
## PctUsePubTrans -0.06793 0.40299 0.11863
## LemasPctOfficDrugUn 0.01209 0.21032 0.08537
## agePct22t29 -0.08864 0.51983 0.104884.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
4.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL4.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 208 observations5 robbbPerPop
y_name = 'robbbPerPop'5.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
5.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.000000 1.000000e+00 1.0000
## population 0.24085 0.000000 1.000000e+00 0.0000
## householdsize 0.13301 1.000000 0.000000e+00 1.0000
## racepctblack 0.99904 1.000000 1.000000e+00 1.0000
## racePctWhite 0.27602 0.000000 0.000000e+00 0.0000
## racePctAsian 0.24028 0.000000 0.000000e+00 0.0000
## racePctHisp 0.21524 0.000000 1.000000e+00 0.0000
## agePct12t29 0.34973 0.000000 0.000000e+00 0.0000
## agePct65up 0.16513 0.000000 1.000000e+00 0.0000
## numbUrban 0.68399 0.000000 1.000000e+00 1.0000
## pctUrban 0.32353 1.000000 0.000000e+00 0.0000
## medIncome 0.29082 0.000000 0.000000e+00 0.0000
## pctWWage 0.86470 1.000000 0.000000e+00 1.0000
## pctWFarmSelf 0.19030 0.000000 1.000000e+00 0.0000
## pctWInvInc 0.10909 0.000000 0.000000e+00 0.0000
## pctWSocSec 0.08138 0.000000 0.000000e+00 0.0000
## pctWPubAsst 0.14269 0.000000 0.000000e+00 0.0000
## pctWRetire 0.98991 1.000000 1.000000e+00 1.0000
## medFamInc 0.09101 0.000000 0.000000e+00 0.0000
## whitePerCap 0.21822 0.000000 0.000000e+00 0.0000
## blackPerCap 0.08318 0.000000 0.000000e+00 0.0000
## indianPerCap 0.06973 0.000000 0.000000e+00 0.0000
## AsianPerCap 0.10215 0.000000 0.000000e+00 0.0000
## OtherPerCap 0.14922 0.000000 0.000000e+00 0.0000
## HispPerCap 0.43369 1.000000 1.000000e+00 0.0000
## NumUnderPov 0.21596 0.000000 0.000000e+00 0.0000
## PctPopUnderPov 0.98912 1.000000 1.000000e+00 1.0000
## PctLess9thGrade 0.99997 1.000000 1.000000e+00 1.0000
## PctBSorMore 0.78914 1.000000 1.000000e+00 0.0000
## PctUnemployed 0.20705 0.000000 0.000000e+00 1.0000
## PctEmploy 0.95714 1.000000 1.000000e+00 1.0000
## PctEmplManu 0.29244 0.000000 0.000000e+00 0.0000
## PctEmplProfServ 0.08015 0.000000 0.000000e+00 0.0000
## PctOccupMgmtProf 0.17435 0.000000 0.000000e+00 0.0000
## MalePctNevMarr 0.99370 1.000000 1.000000e+00 1.0000
## TotalPctDiv 0.69694 1.000000 1.000000e+00 1.0000
## PersPerFam 0.77697 1.000000 0.000000e+00 1.0000
## PctFam2Par 0.08394 0.000000 0.000000e+00 0.0000
## PctWorkMom 0.99716 1.000000 1.000000e+00 1.0000
## PctKidsBornNeverMar 0.99956 1.000000 1.000000e+00 1.0000
## NumImmig 0.24117 0.000000 0.000000e+00 0.0000
## PctImmigRecent 0.19211 0.000000 0.000000e+00 0.0000
## PctRecentImmig 0.73653 1.000000 1.000000e+00 1.0000
## PctSpeakEnglOnly 0.15478 0.000000 0.000000e+00 0.0000
## PctNotSpeakEnglWell 0.12281 0.000000 0.000000e+00 0.0000
## PctLargHouseFam 0.12676 0.000000 0.000000e+00 0.0000
## PersPerOccupHous 0.99500 1.000000 1.000000e+00 1.0000
## PersPerOwnOccHous 0.99668 1.000000 1.000000e+00 1.0000
## PersPerRentOccHous 0.99989 1.000000 1.000000e+00 1.0000
## PctPersOwnOccup 0.99900 1.000000 1.000000e+00 1.0000
## PctPersDenseHous 0.99959 1.000000 1.000000e+00 1.0000
## PctHousLess3BR 0.12767 0.000000 0.000000e+00 0.0000
## MedNumBR 0.05615 0.000000 0.000000e+00 0.0000
## HousVacant 0.67723 1.000000 1.000000e+00 1.0000
## PctHousOccup 0.09513 0.000000 0.000000e+00 0.0000
## PctHousOwnOcc 0.99914 1.000000 1.000000e+00 1.0000
## PctVacantBoarded 0.99870 1.000000 1.000000e+00 1.0000
## PctVacMore6Mos 0.11004 0.000000 0.000000e+00 0.0000
## MedYrHousBuilt 0.77810 1.000000 0.000000e+00 1.0000
## PctHousNoPhone 0.08553 0.000000 0.000000e+00 0.0000
## PctWOFullPlumb 0.07816 0.000000 0.000000e+00 0.0000
## OwnOccLowQuart 0.12014 0.000000 0.000000e+00 0.0000
## OwnOccMedVal 0.18672 0.000000 0.000000e+00 0.0000
## OwnOccHiQuart 0.82844 1.000000 1.000000e+00 1.0000
## RentLowQ 0.10712 0.000000 0.000000e+00 0.0000
## RentMedian 0.09698 0.000000 0.000000e+00 0.0000
## RentHighQ 0.57972 0.000000 0.000000e+00 0.0000
## MedRent 0.53887 0.000000 0.000000e+00 0.0000
## MedRentPctHousInc 0.19178 1.000000 0.000000e+00 0.0000
## MedOwnCostPctInc 0.07612 0.000000 0.000000e+00 0.0000
## MedOwnCostPctIncNoMtg 0.99954 1.000000 1.000000e+00 1.0000
## NumInShelters 0.07989 0.000000 0.000000e+00 0.0000
## NumStreet 0.99969 1.000000 1.000000e+00 1.0000
## PctForeignBorn 0.96635 1.000000 1.000000e+00 1.0000
## PctBornSameState 0.21831 0.000000 0.000000e+00 0.0000
## PctSameHouse85 0.07417 0.000000 0.000000e+00 0.0000
## PctSameCity85 0.07479 0.000000 0.000000e+00 0.0000
## PctSameState85 0.09936 0.000000 0.000000e+00 0.0000
## LandArea 0.07856 0.000000 0.000000e+00 0.0000
## PopDens 0.06313 0.000000 0.000000e+00 0.0000
## PctUsePubTrans 0.95855 1.000000 1.000000e+00 1.0000
## LemasPctOfficDrugUn 0.32886 1.000000 0.000000e+00 0.0000
## agePct22t29 0.99750 1.000000 1.000000e+00 1.0000
## BF NA 0.173467 4.292394e-03 1.0000
## PostProbs NA 0.000700 6.000000e-04 0.0006
## R2 NA 0.769100 7.668000e-01 0.7674
## dim NA 34.000000 3.200000e+01 31.0000
## logmarg NA 1285.111136 1.281412e+03 1286.8629
## model 4 model 5
## Intercept 1.000000e+00 1.000000e+00
## population 0.000000e+00 0.000000e+00
## householdsize 0.000000e+00 0.000000e+00
## racepctblack 1.000000e+00 1.000000e+00
## racePctWhite 0.000000e+00 0.000000e+00
## racePctAsian 0.000000e+00 0.000000e+00
## racePctHisp 0.000000e+00 0.000000e+00
## agePct12t29 1.000000e+00 1.000000e+00
## agePct65up 0.000000e+00 0.000000e+00
## numbUrban 0.000000e+00 1.000000e+00
## pctUrban 1.000000e+00 1.000000e+00
## medIncome 0.000000e+00 1.000000e+00
## pctWWage 1.000000e+00 1.000000e+00
## pctWFarmSelf 0.000000e+00 0.000000e+00
## pctWInvInc 0.000000e+00 0.000000e+00
## pctWSocSec 1.000000e+00 0.000000e+00
## pctWPubAsst 0.000000e+00 0.000000e+00
## pctWRetire 1.000000e+00 1.000000e+00
## medFamInc 0.000000e+00 0.000000e+00
## whitePerCap 0.000000e+00 0.000000e+00
## blackPerCap 0.000000e+00 0.000000e+00
## indianPerCap 0.000000e+00 0.000000e+00
## AsianPerCap 0.000000e+00 0.000000e+00
## OtherPerCap 0.000000e+00 0.000000e+00
## HispPerCap 0.000000e+00 0.000000e+00
## NumUnderPov 1.000000e+00 0.000000e+00
## PctPopUnderPov 1.000000e+00 1.000000e+00
## PctLess9thGrade 1.000000e+00 1.000000e+00
## PctBSorMore 1.000000e+00 1.000000e+00
## PctUnemployed 1.000000e+00 0.000000e+00
## PctEmploy 1.000000e+00 1.000000e+00
## PctEmplManu 0.000000e+00 0.000000e+00
## PctEmplProfServ 0.000000e+00 0.000000e+00
## PctOccupMgmtProf 0.000000e+00 0.000000e+00
## MalePctNevMarr 1.000000e+00 1.000000e+00
## TotalPctDiv 1.000000e+00 0.000000e+00
## PersPerFam 1.000000e+00 1.000000e+00
## PctFam2Par 0.000000e+00 0.000000e+00
## PctWorkMom 1.000000e+00 1.000000e+00
## PctKidsBornNeverMar 1.000000e+00 1.000000e+00
## NumImmig 0.000000e+00 0.000000e+00
## PctImmigRecent 0.000000e+00 0.000000e+00
## PctRecentImmig 1.000000e+00 1.000000e+00
## PctSpeakEnglOnly 0.000000e+00 0.000000e+00
## PctNotSpeakEnglWell 0.000000e+00 0.000000e+00
## PctLargHouseFam 0.000000e+00 0.000000e+00
## PersPerOccupHous 1.000000e+00 1.000000e+00
## PersPerOwnOccHous 1.000000e+00 1.000000e+00
## PersPerRentOccHous 1.000000e+00 1.000000e+00
## PctPersOwnOccup 1.000000e+00 1.000000e+00
## PctPersDenseHous 1.000000e+00 1.000000e+00
## PctHousLess3BR 0.000000e+00 0.000000e+00
## MedNumBR 0.000000e+00 0.000000e+00
## HousVacant 0.000000e+00 0.000000e+00
## PctHousOccup 0.000000e+00 0.000000e+00
## PctHousOwnOcc 1.000000e+00 1.000000e+00
## PctVacantBoarded 1.000000e+00 1.000000e+00
## PctVacMore6Mos 0.000000e+00 0.000000e+00
## MedYrHousBuilt 0.000000e+00 1.000000e+00
## PctHousNoPhone 0.000000e+00 0.000000e+00
## PctWOFullPlumb 0.000000e+00 0.000000e+00
## OwnOccLowQuart 0.000000e+00 0.000000e+00
## OwnOccMedVal 0.000000e+00 0.000000e+00
## OwnOccHiQuart 1.000000e+00 1.000000e+00
## RentLowQ 0.000000e+00 0.000000e+00
## RentMedian 0.000000e+00 0.000000e+00
## RentHighQ 0.000000e+00 1.000000e+00
## MedRent 0.000000e+00 1.000000e+00
## MedRentPctHousInc 0.000000e+00 0.000000e+00
## MedOwnCostPctInc 0.000000e+00 0.000000e+00
## MedOwnCostPctIncNoMtg 1.000000e+00 1.000000e+00
## NumInShelters 0.000000e+00 0.000000e+00
## NumStreet 1.000000e+00 1.000000e+00
## PctForeignBorn 1.000000e+00 1.000000e+00
## PctBornSameState 0.000000e+00 1.000000e+00
## PctSameHouse85 0.000000e+00 0.000000e+00
## PctSameCity85 0.000000e+00 0.000000e+00
## PctSameState85 0.000000e+00 0.000000e+00
## LandArea 0.000000e+00 0.000000e+00
## PopDens 0.000000e+00 0.000000e+00
## PctUsePubTrans 1.000000e+00 1.000000e+00
## LemasPctOfficDrugUn 0.000000e+00 0.000000e+00
## agePct22t29 1.000000e+00 1.000000e+00
## BF 7.292435e-03 3.304046e-02
## PostProbs 6.000000e-04 6.000000e-04
## R2 7.669000e-01 7.686000e-01
## dim 3.200000e+01 3.400000e+01
## logmarg 1.281942e+03 1.283453e+03top 5 model
5.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
5.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 16612 models
## post mean post SD post p(B != 0)
## Intercept 166.76597 2.63232 1.00000
## population 2.66367 5.83202 0.24085
## householdsize -1.81116 6.36137 0.13301
## racepctblack 62.91057 12.84826 0.99904
## racePctWhite 7.15016 14.47977 0.27602
## racePctAsian 2.34387 5.24842 0.24028
## racePctHisp -3.53246 8.84466 0.21524
## agePct12t29 -8.04223 12.90874 0.34973
## agePct65up 2.58321 8.12784 0.16513
## numbUrban 9.91987 9.93354 0.68399
## pctUrban 1.41901 8.35297 0.32353
## medIncome -9.62829 19.15903 0.29082
## pctWWage -33.06844 17.56991 0.86470
## pctWFarmSelf 1.01734 2.59224 0.19030
## pctWInvInc -0.94201 4.50484 0.10909
## pctWSocSec -0.06230 4.63883 0.08138
## pctWPubAsst 1.62051 5.27083 0.14269
## pctWRetire -20.94698 5.68346 0.98991
## medFamInc 0.48294 9.72950 0.09101
## whitePerCap 4.06247 9.83678 0.21822
## blackPerCap 0.21111 1.14992 0.08318
## indianPerCap 0.07367 0.74448 0.06973
## AsianPerCap 0.29755 1.34663 0.10215
## OtherPerCap 0.58110 1.79534 0.14922
## HispPerCap 3.57827 4.78423 0.43369
## NumUnderPov 2.85408 7.07316 0.21596
## PctPopUnderPov -44.83369 12.23251 0.98912
## PctLess9thGrade -32.34239 7.32333 0.99997
## PctBSorMore -19.35995 13.62785 0.78914
## PctUnemployed -2.42446 5.91724 0.20705
## PctEmploy 38.73775 13.51790 0.95714
## PctEmplManu -2.10635 3.88208 0.29244
## PctEmplProfServ -0.18482 2.04511 0.08015
## PctOccupMgmtProf 1.95648 7.61442 0.17435
## MalePctNevMarr 44.70827 11.39520 0.99370
## TotalPctDiv 13.70459 11.04227 0.69694
## PersPerFam -36.18711 24.88698 0.77697
## PctFam2Par 0.42748 5.35716 0.08394
## PctWorkMom -23.32350 4.99821 0.99716
## PctKidsBornNeverMar 89.10967 8.35934 0.99956
## NumImmig 3.32219 7.34897 0.24117
## PctImmigRecent -1.19324 3.03723 0.19211
## PctRecentImmig -16.78310 12.33228 0.73653
## PctSpeakEnglOnly -2.70058 9.31974 0.15478
## PctNotSpeakEnglWell 1.68246 6.59471 0.12281
## PctLargHouseFam 1.58361 6.80657 0.12676
## PersPerOccupHous -155.01210 39.28298 0.99500
## PersPerOwnOccHous 190.08991 27.84114 0.99668
## PersPerRentOccHous -71.68713 14.04647 0.99989
## PctPersOwnOccup -564.88203 77.20236 0.99900
## PctPersDenseHous 73.48860 12.20112 0.99959
## PctHousLess3BR 0.99261 3.95279 0.12767
## MedNumBR -0.01674 0.96318 0.05615
## HousVacant 6.95871 5.82044 0.67723
## PctHousOccup -0.19946 1.30995 0.09513
## PctHousOwnOcc 562.83647 76.25477 0.99914
## PctVacantBoarded 23.34907 4.10103 0.99870
## PctVacMore6Mos -0.45115 1.84260 0.11004
## MedYrHousBuilt -10.33985 7.03420 0.77810
## PctHousNoPhone -0.30792 2.31076 0.08553
## PctWOFullPlumb 0.12180 1.06354 0.07816
## OwnOccLowQuart -1.22241 7.13952 0.12014
## OwnOccMedVal -3.19720 11.62184 0.18672
## OwnOccHiQuart -28.17365 15.79939 0.82844
## RentLowQ -0.99441 4.83726 0.10712
## RentMedian 1.61968 9.22497 0.09698
## RentHighQ -27.89292 28.34398 0.57972
## MedRent 24.84778 27.06503 0.53887
## MedRentPctHousInc 1.31697 3.34885 0.19178
## MedOwnCostPctInc 0.07004 1.51098 0.07612
## MedOwnCostPctIncNoMtg -19.69044 3.75097 0.99954
## NumInShelters 0.21699 1.40123 0.07989
## NumStreet 30.63339 4.05005 0.99969
## PctForeignBorn 48.13008 16.82732 0.96635
## PctBornSameState -1.91729 4.59612 0.21831
## PctSameHouse85 -0.15342 2.34591 0.07417
## PctSameCity85 0.11067 1.71636 0.07479
## PctSameState85 0.25618 2.40880 0.09936
## LandArea -0.24390 1.86561 0.07856
## PopDens -0.12720 1.46533 0.06313
## PctUsePubTrans 14.97322 5.56829 0.95855
## LemasPctOfficDrugUn 2.15780 3.57912 0.32886
## agePct22t29 -30.85116 6.92896 0.997505.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
5.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL5.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 1 observations6 assaultPerPop
y_name = 'assaultPerPop'6.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
6.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.00000 1.00000000 1.000000e+00
## population 0.22884 0.00000 0.00000000 0.000000e+00
## householdsize 0.12883 1.00000 0.00000000 1.000000e+00
## racepctblack 0.69834 0.00000 1.00000000 0.000000e+00
## racePctWhite 0.24563 1.00000 0.00000000 1.000000e+00
## racePctAsian 0.11769 0.00000 0.00000000 0.000000e+00
## racePctHisp 0.32476 0.00000 1.00000000 0.000000e+00
## agePct12t29 0.70974 1.00000 1.00000000 1.000000e+00
## agePct65up 0.11178 0.00000 0.00000000 0.000000e+00
## numbUrban 0.34357 1.00000 0.00000000 0.000000e+00
## pctUrban 0.31701 0.00000 1.00000000 1.000000e+00
## medIncome 0.10371 0.00000 0.00000000 0.000000e+00
## pctWWage 0.26063 0.00000 0.00000000 0.000000e+00
## pctWFarmSelf 0.10830 0.00000 0.00000000 0.000000e+00
## pctWInvInc 0.99822 1.00000 1.00000000 1.000000e+00
## pctWSocSec 0.20756 1.00000 0.00000000 0.000000e+00
## pctWPubAsst 0.12102 0.00000 0.00000000 0.000000e+00
## pctWRetire 0.72934 1.00000 1.00000000 0.000000e+00
## medFamInc 0.11702 0.00000 0.00000000 0.000000e+00
## whitePerCap 0.10249 0.00000 0.00000000 0.000000e+00
## blackPerCap 0.09683 0.00000 0.00000000 0.000000e+00
## indianPerCap 0.07663 0.00000 0.00000000 0.000000e+00
## AsianPerCap 0.38496 1.00000 1.00000000 0.000000e+00
## OtherPerCap 0.71102 1.00000 1.00000000 0.000000e+00
## HispPerCap 0.18313 0.00000 0.00000000 1.000000e+00
## NumUnderPov 0.14849 0.00000 0.00000000 0.000000e+00
## PctPopUnderPov 0.11726 0.00000 0.00000000 0.000000e+00
## PctLess9thGrade 0.10829 0.00000 1.00000000 0.000000e+00
## PctBSorMore 0.14173 0.00000 0.00000000 0.000000e+00
## PctUnemployed 0.09701 0.00000 0.00000000 0.000000e+00
## PctEmploy 0.11627 0.00000 0.00000000 0.000000e+00
## PctEmplManu 0.23949 0.00000 0.00000000 0.000000e+00
## PctEmplProfServ 0.10458 0.00000 0.00000000 0.000000e+00
## PctOccupMgmtProf 0.14689 0.00000 0.00000000 0.000000e+00
## MalePctNevMarr 0.21968 0.00000 0.00000000 0.000000e+00
## TotalPctDiv 0.16270 0.00000 1.00000000 0.000000e+00
## PersPerFam 0.12112 0.00000 0.00000000 0.000000e+00
## PctFam2Par 0.68856 1.00000 1.00000000 1.000000e+00
## PctWorkMom 0.31405 0.00000 0.00000000 0.000000e+00
## PctKidsBornNeverMar 0.93743 1.00000 1.00000000 1.000000e+00
## NumImmig 0.52785 0.00000 0.00000000 0.000000e+00
## PctImmigRecent 0.09215 0.00000 0.00000000 0.000000e+00
## PctRecentImmig 0.11802 0.00000 0.00000000 0.000000e+00
## PctSpeakEnglOnly 0.19388 0.00000 0.00000000 0.000000e+00
## PctNotSpeakEnglWell 0.97467 1.00000 1.00000000 1.000000e+00
## PctLargHouseFam 0.11835 0.00000 0.00000000 0.000000e+00
## PersPerOccupHous 0.35375 0.00000 0.00000000 0.000000e+00
## PersPerOwnOccHous 0.67624 1.00000 1.00000000 1.000000e+00
## PersPerRentOccHous 0.29164 0.00000 0.00000000 0.000000e+00
## PctPersOwnOccup 0.32868 0.00000 0.00000000 0.000000e+00
## PctPersDenseHous 0.97769 1.00000 1.00000000 1.000000e+00
## PctHousLess3BR 0.11822 0.00000 0.00000000 0.000000e+00
## MedNumBR 0.09068 0.00000 0.00000000 0.000000e+00
## HousVacant 0.08434 0.00000 0.00000000 0.000000e+00
## PctHousOccup 0.90593 1.00000 1.00000000 1.000000e+00
## PctHousOwnOcc 0.33965 0.00000 0.00000000 0.000000e+00
## PctVacantBoarded 0.35965 0.00000 0.00000000 0.000000e+00
## PctVacMore6Mos 0.22355 0.00000 0.00000000 0.000000e+00
## MedYrHousBuilt 0.14705 0.00000 0.00000000 1.000000e+00
## PctHousNoPhone 0.29231 0.00000 0.00000000 1.000000e+00
## PctWOFullPlumb 0.09005 0.00000 0.00000000 0.000000e+00
## OwnOccLowQuart 0.09121 0.00000 0.00000000 0.000000e+00
## OwnOccMedVal 0.09230 0.00000 0.00000000 0.000000e+00
## OwnOccHiQuart 0.09283 0.00000 0.00000000 0.000000e+00
## RentLowQ 0.83882 1.00000 1.00000000 1.000000e+00
## RentMedian 0.25138 0.00000 0.00000000 0.000000e+00
## RentHighQ 0.18862 1.00000 0.00000000 1.000000e+00
## MedRent 0.53421 0.00000 1.00000000 0.000000e+00
## MedRentPctHousInc 0.09149 0.00000 0.00000000 0.000000e+00
## MedOwnCostPctInc 0.11898 0.00000 0.00000000 0.000000e+00
## MedOwnCostPctIncNoMtg 0.51395 0.00000 1.00000000 0.000000e+00
## NumInShelters 0.14231 0.00000 0.00000000 0.000000e+00
## NumStreet 0.99944 1.00000 1.00000000 1.000000e+00
## PctForeignBorn 0.19998 0.00000 1.00000000 0.000000e+00
## PctBornSameState 0.11822 0.00000 0.00000000 0.000000e+00
## PctSameHouse85 0.14555 0.00000 0.00000000 0.000000e+00
## PctSameCity85 0.15789 0.00000 0.00000000 0.000000e+00
## PctSameState85 0.11912 0.00000 0.00000000 0.000000e+00
## LandArea 0.14014 0.00000 0.00000000 0.000000e+00
## PopDens 0.54734 1.00000 1.00000000 1.000000e+00
## PctUsePubTrans 0.20710 0.00000 0.00000000 0.000000e+00
## LemasPctOfficDrugUn 0.09826 0.00000 0.00000000 0.000000e+00
## agePct22t29 0.20048 0.00000 0.00000000 0.000000e+00
## BF NA 0.11119 0.04132928 2.758002e-03
## PostProbs NA 0.00050 0.00040000 4.000000e-04
## R2 NA 0.49250 0.49620000 4.891000e-01
## dim NA 20.00000 23.00000000 1.900000e+01
## logmarg NA 584.94858 583.95890954 5.812518e+02
## model 4 model 5
## Intercept 1.000000e+00 1.0000
## population 0.000000e+00 0.0000
## householdsize 0.000000e+00 0.0000
## racepctblack 1.000000e+00 1.0000
## racePctWhite 0.000000e+00 0.0000
## racePctAsian 0.000000e+00 0.0000
## racePctHisp 1.000000e+00 0.0000
## agePct12t29 1.000000e+00 1.0000
## agePct65up 0.000000e+00 0.0000
## numbUrban 0.000000e+00 0.0000
## pctUrban 1.000000e+00 1.0000
## medIncome 0.000000e+00 0.0000
## pctWWage 0.000000e+00 0.0000
## pctWFarmSelf 0.000000e+00 0.0000
## pctWInvInc 1.000000e+00 1.0000
## pctWSocSec 1.000000e+00 0.0000
## pctWPubAsst 1.000000e+00 0.0000
## pctWRetire 1.000000e+00 1.0000
## medFamInc 1.000000e+00 0.0000
## whitePerCap 0.000000e+00 0.0000
## blackPerCap 0.000000e+00 0.0000
## indianPerCap 0.000000e+00 0.0000
## AsianPerCap 1.000000e+00 1.0000
## OtherPerCap 1.000000e+00 1.0000
## HispPerCap 0.000000e+00 0.0000
## NumUnderPov 1.000000e+00 0.0000
## PctPopUnderPov 0.000000e+00 0.0000
## PctLess9thGrade 0.000000e+00 0.0000
## PctBSorMore 0.000000e+00 0.0000
## PctUnemployed 0.000000e+00 0.0000
## PctEmploy 0.000000e+00 0.0000
## PctEmplManu 0.000000e+00 0.0000
## PctEmplProfServ 0.000000e+00 0.0000
## PctOccupMgmtProf 0.000000e+00 0.0000
## MalePctNevMarr 1.000000e+00 0.0000
## TotalPctDiv 0.000000e+00 0.0000
## PersPerFam 0.000000e+00 0.0000
## PctFam2Par 1.000000e+00 1.0000
## PctWorkMom 0.000000e+00 1.0000
## PctKidsBornNeverMar 1.000000e+00 1.0000
## NumImmig 1.000000e+00 0.0000
## PctImmigRecent 0.000000e+00 0.0000
## PctRecentImmig 0.000000e+00 0.0000
## PctSpeakEnglOnly 0.000000e+00 1.0000
## PctNotSpeakEnglWell 1.000000e+00 1.0000
## PctLargHouseFam 0.000000e+00 0.0000
## PersPerOccupHous 0.000000e+00 0.0000
## PersPerOwnOccHous 0.000000e+00 1.0000
## PersPerRentOccHous 1.000000e+00 0.0000
## PctPersOwnOccup 1.000000e+00 0.0000
## PctPersDenseHous 1.000000e+00 1.0000
## PctHousLess3BR 0.000000e+00 0.0000
## MedNumBR 0.000000e+00 0.0000
## HousVacant 0.000000e+00 0.0000
## PctHousOccup 1.000000e+00 1.0000
## PctHousOwnOcc 1.000000e+00 0.0000
## PctVacantBoarded 0.000000e+00 1.0000
## PctVacMore6Mos 0.000000e+00 0.0000
## MedYrHousBuilt 0.000000e+00 0.0000
## PctHousNoPhone 0.000000e+00 0.0000
## PctWOFullPlumb 0.000000e+00 0.0000
## OwnOccLowQuart 0.000000e+00 0.0000
## OwnOccMedVal 0.000000e+00 0.0000
## OwnOccHiQuart 0.000000e+00 0.0000
## RentLowQ 1.000000e+00 1.0000
## RentMedian 1.000000e+00 0.0000
## RentHighQ 0.000000e+00 0.0000
## MedRent 0.000000e+00 1.0000
## MedRentPctHousInc 0.000000e+00 0.0000
## MedOwnCostPctInc 0.000000e+00 0.0000
## MedOwnCostPctIncNoMtg 0.000000e+00 1.0000
## NumInShelters 1.000000e+00 0.0000
## NumStreet 1.000000e+00 1.0000
## PctForeignBorn 0.000000e+00 0.0000
## PctBornSameState 0.000000e+00 0.0000
## PctSameHouse85 0.000000e+00 0.0000
## PctSameCity85 0.000000e+00 0.0000
## PctSameState85 0.000000e+00 0.0000
## LandArea 0.000000e+00 0.0000
## PopDens 0.000000e+00 1.0000
## PctUsePubTrans 1.000000e+00 0.0000
## LemasPctOfficDrugUn 0.000000e+00 0.0000
## agePct22t29 1.000000e+00 0.0000
## BF 4.544706e-07 1.0000
## PostProbs 4.000000e-04 0.0004
## R2 4.982000e-01 0.4965
## dim 2.900000e+01 22.0000
## logmarg 5.725410e+02 587.1451top 5 model
6.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
6.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 27177 models
## post mean post SD post p(B != 0)
## Intercept 374.70427 6.68862 1.00000
## population -7.20662 18.63811 0.22884
## householdsize 0.55810 9.85411 0.12883
## racepctblack 32.76431 26.49645 0.69834
## racePctWhite -8.12580 19.42643 0.24563
## racePctAsian -0.80993 4.77867 0.11769
## racePctHisp 12.41428 21.44071 0.32476
## agePct12t29 -29.75835 26.55547 0.70974
## agePct65up 1.29601 10.06931 0.11178
## numbUrban 6.49990 13.23122 0.34357
## pctUrban 6.23957 12.51196 0.31701
## medIncome 2.81504 14.59791 0.10371
## pctWWage -9.25242 19.79404 0.26063
## pctWFarmSelf 0.41148 3.14187 0.10830
## pctWInvInc -85.02458 22.96546 0.99822
## pctWSocSec 6.37727 16.56620 0.20756
## pctWPubAsst 1.95133 8.78632 0.12102
## pctWRetire -21.47679 16.60236 0.72934
## medFamInc 1.72536 12.74148 0.11702
## whitePerCap 0.23487 7.67170 0.10249
## blackPerCap -0.67872 3.21487 0.09683
## indianPerCap -0.13600 1.89588 0.07663
## AsianPerCap 6.04234 9.09630 0.38496
## OtherPerCap 13.67158 10.62906 0.71102
## HispPerCap 2.47788 6.80861 0.18313
## NumUnderPov -1.66370 13.92155 0.14849
## PctPopUnderPov -0.50972 10.31127 0.11726
## PctLess9thGrade 1.42960 7.68080 0.10829
## PctBSorMore 2.40462 10.47981 0.14173
## PctUnemployed -0.97078 5.98649 0.09701
## PctEmploy -0.07083 8.45118 0.11627
## PctEmplManu -3.48227 7.64211 0.23949
## PctEmplProfServ -0.54026 4.91836 0.10458
## PctOccupMgmtProf 3.23855 11.02576 0.14689
## MalePctNevMarr 5.46315 18.56939 0.21968
## TotalPctDiv -0.73925 11.81192 0.16270
## PersPerFam 2.85376 16.44289 0.12112
## PctFam2Par -52.00146 44.07666 0.68856
## PctWorkMom -5.59939 9.96053 0.31405
## PctKidsBornNeverMar 76.51008 32.02011 0.93743
## NumImmig 24.37726 29.54705 0.52785
## PctImmigRecent -0.28782 2.94373 0.09215
## PctRecentImmig -1.87663 8.77889 0.11802
## PctSpeakEnglOnly -5.23182 16.98263 0.19388
## PctNotSpeakEnglWell -86.80345 31.44144 0.97467
## PctLargHouseFam -2.13334 10.65830 0.11835
## PersPerOccupHous 27.68085 51.42329 0.35375
## PersPerOwnOccHous -47.27123 44.60627 0.67624
## PersPerRentOccHous -15.02904 29.85264 0.29164
## PctPersOwnOccup -76.48118 140.21452 0.32868
## PctPersDenseHous 93.27523 29.81227 0.97769
## PctHousLess3BR 1.96796 9.01438 0.11822
## MedNumBR -0.49485 3.44420 0.09068
## HousVacant -0.41956 3.18511 0.08434
## PctHousOccup -24.26747 11.58629 0.90593
## PctHousOwnOcc 69.43228 130.47776 0.33965
## PctVacantBoarded 6.91463 11.00599 0.35965
## PctVacMore6Mos -3.61813 8.32075 0.22355
## MedYrHousBuilt 2.09065 7.31535 0.14705
## PctHousNoPhone 8.38583 15.60851 0.29231
## PctWOFullPlumb -0.53629 3.20824 0.09005
## OwnOccLowQuart 0.91189 8.21787 0.09121
## OwnOccMedVal 0.37935 8.66237 0.09230
## OwnOccHiQuart 0.23307 7.01888 0.09283
## RentLowQ -71.25901 41.58933 0.83882
## RentMedian 19.02320 42.56626 0.25138
## RentHighQ 8.92775 24.85031 0.18862
## MedRent 47.34124 51.54773 0.53421
## MedRentPctHousInc -0.12809 3.32187 0.09149
## MedOwnCostPctInc -1.42727 5.87969 0.11898
## MedOwnCostPctIncNoMtg -10.71670 12.43469 0.51395
## NumInShelters 1.47406 5.41465 0.14231
## NumStreet 44.00144 9.71786 0.99944
## PctForeignBorn 6.78644 19.38718 0.19998
## PctBornSameState 0.59927 4.54076 0.11822
## PctSameHouse85 2.42145 8.85619 0.14555
## PctSameCity85 2.54845 8.24808 0.15789
## PctSameState85 1.08798 4.88852 0.11912
## LandArea 1.43458 6.92917 0.14014
## PopDens -13.85212 14.99277 0.54734
## PctUsePubTrans -3.32780 8.24665 0.20710
## LemasPctOfficDrugUn 0.60801 3.10082 0.09826
## agePct22t29 -4.19196 11.14075 0.200486.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
6.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL6.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 13 observations7 burglPerPop
y_name = 'burglPerPop'7.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
7.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.00000000 1.000000e+00 1.00000000
## population 0.18091 0.00000000 1.000000e+00 1.00000000
## householdsize 0.89274 1.00000000 0.000000e+00 1.00000000
## racepctblack 0.96108 1.00000000 1.000000e+00 1.00000000
## racePctWhite 0.09902 0.00000000 0.000000e+00 0.00000000
## racePctAsian 0.10389 0.00000000 0.000000e+00 0.00000000
## racePctHisp 0.14769 0.00000000 0.000000e+00 0.00000000
## agePct12t29 0.28871 0.00000000 0.000000e+00 0.00000000
## agePct65up 0.16634 0.00000000 0.000000e+00 0.00000000
## numbUrban 0.35407 1.00000000 0.000000e+00 0.00000000
## pctUrban 0.49945 0.00000000 0.000000e+00 0.00000000
## medIncome 0.09063 0.00000000 0.000000e+00 0.00000000
## pctWWage 0.12374 0.00000000 0.000000e+00 0.00000000
## pctWFarmSelf 0.07145 0.00000000 0.000000e+00 0.00000000
## pctWInvInc 0.46062 0.00000000 0.000000e+00 0.00000000
## pctWSocSec 0.87530 1.00000000 1.000000e+00 1.00000000
## pctWPubAsst 0.46020 1.00000000 0.000000e+00 1.00000000
## pctWRetire 0.98374 1.00000000 1.000000e+00 1.00000000
## medFamInc 0.11418 0.00000000 0.000000e+00 0.00000000
## whitePerCap 0.99026 1.00000000 1.000000e+00 1.00000000
## blackPerCap 0.08740 0.00000000 0.000000e+00 0.00000000
## indianPerCap 0.09180 0.00000000 0.000000e+00 0.00000000
## AsianPerCap 0.07523 0.00000000 0.000000e+00 0.00000000
## OtherPerCap 0.28600 0.00000000 1.000000e+00 0.00000000
## HispPerCap 0.11045 0.00000000 0.000000e+00 0.00000000
## NumUnderPov 0.15994 0.00000000 0.000000e+00 0.00000000
## PctPopUnderPov 0.13281 0.00000000 1.000000e+00 0.00000000
## PctLess9thGrade 0.70854 1.00000000 0.000000e+00 1.00000000
## PctBSorMore 0.13210 0.00000000 1.000000e+00 0.00000000
## PctUnemployed 0.09563 1.00000000 0.000000e+00 0.00000000
## PctEmploy 0.39009 0.00000000 1.000000e+00 1.00000000
## PctEmplManu 0.20842 0.00000000 0.000000e+00 0.00000000
## PctEmplProfServ 0.09711 0.00000000 0.000000e+00 0.00000000
## PctOccupMgmtProf 0.39280 0.00000000 1.000000e+00 0.00000000
## MalePctNevMarr 0.99244 1.00000000 1.000000e+00 1.00000000
## TotalPctDiv 0.97465 1.00000000 1.000000e+00 1.00000000
## PersPerFam 0.20855 0.00000000 0.000000e+00 0.00000000
## PctFam2Par 0.30995 0.00000000 1.000000e+00 0.00000000
## PctWorkMom 0.29563 0.00000000 1.000000e+00 1.00000000
## PctKidsBornNeverMar 0.61733 1.00000000 0.000000e+00 1.00000000
## NumImmig 0.70538 0.00000000 1.000000e+00 1.00000000
## PctImmigRecent 0.11919 0.00000000 0.000000e+00 0.00000000
## PctRecentImmig 0.79777 1.00000000 0.000000e+00 1.00000000
## PctSpeakEnglOnly 0.26757 0.00000000 0.000000e+00 0.00000000
## PctNotSpeakEnglWell 0.14905 0.00000000 0.000000e+00 0.00000000
## PctLargHouseFam 0.13885 0.00000000 1.000000e+00 0.00000000
## PersPerOccupHous 0.92578 1.00000000 0.000000e+00 1.00000000
## PersPerOwnOccHous 0.62694 0.00000000 0.000000e+00 0.00000000
## PersPerRentOccHous 0.30072 0.00000000 0.000000e+00 0.00000000
## PctPersOwnOccup 0.49837 1.00000000 1.000000e+00 1.00000000
## PctPersDenseHous 0.35755 0.00000000 0.000000e+00 0.00000000
## PctHousLess3BR 0.10954 0.00000000 0.000000e+00 1.00000000
## MedNumBR 0.16149 0.00000000 0.000000e+00 0.00000000
## HousVacant 0.43073 0.00000000 0.000000e+00 1.00000000
## PctHousOccup 0.99917 1.00000000 1.000000e+00 1.00000000
## PctHousOwnOcc 0.49741 1.00000000 1.000000e+00 1.00000000
## PctVacantBoarded 0.17623 0.00000000 0.000000e+00 0.00000000
## PctVacMore6Mos 0.89907 0.00000000 1.000000e+00 1.00000000
## MedYrHousBuilt 0.15693 0.00000000 0.000000e+00 0.00000000
## PctHousNoPhone 0.73584 1.00000000 0.000000e+00 1.00000000
## PctWOFullPlumb 0.07007 0.00000000 0.000000e+00 0.00000000
## OwnOccLowQuart 0.12070 0.00000000 0.000000e+00 0.00000000
## OwnOccMedVal 0.12010 0.00000000 0.000000e+00 0.00000000
## OwnOccHiQuart 0.34339 1.00000000 0.000000e+00 0.00000000
## RentLowQ 0.60429 0.00000000 1.000000e+00 0.00000000
## RentMedian 0.14430 1.00000000 0.000000e+00 0.00000000
## RentHighQ 0.84994 0.00000000 1.000000e+00 1.00000000
## MedRent 0.42824 0.00000000 1.000000e+00 0.00000000
## MedRentPctHousInc 0.85814 1.00000000 1.000000e+00 1.00000000
## MedOwnCostPctInc 0.08788 0.00000000 0.000000e+00 0.00000000
## MedOwnCostPctIncNoMtg 0.08498 0.00000000 1.000000e+00 0.00000000
## NumInShelters 0.10264 0.00000000 1.000000e+00 0.00000000
## NumStreet 0.97489 1.00000000 1.000000e+00 1.00000000
## PctForeignBorn 0.77244 1.00000000 0.000000e+00 1.00000000
## PctBornSameState 0.13626 0.00000000 0.000000e+00 0.00000000
## PctSameHouse85 0.20324 1.00000000 0.000000e+00 0.00000000
## PctSameCity85 0.12435 0.00000000 0.000000e+00 0.00000000
## PctSameState85 0.09740 0.00000000 0.000000e+00 0.00000000
## LandArea 0.12276 0.00000000 0.000000e+00 0.00000000
## PopDens 0.57622 1.00000000 0.000000e+00 0.00000000
## PctUsePubTrans 0.80152 1.00000000 1.000000e+00 1.00000000
## LemasPctOfficDrugUn 0.08598 0.00000000 0.000000e+00 0.00000000
## agePct22t29 0.20962 0.00000000 0.000000e+00 0.00000000
## BF NA 0.03618418 6.127948e-05 0.03385791
## PostProbs NA 0.00060000 6.000000e-04 0.00050000
## R2 NA 0.56530000 5.647000e-01 0.56770000
## dim NA 27.00000000 2.900000e+01 29.00000000
## logmarg NA 712.17299899 7.057921e+02 712.10654953
## model 4 model 5
## Intercept 1.0000 1.0000000
## population 0.0000 0.0000000
## householdsize 1.0000 1.0000000
## racepctblack 1.0000 1.0000000
## racePctWhite 0.0000 0.0000000
## racePctAsian 0.0000 0.0000000
## racePctHisp 0.0000 0.0000000
## agePct12t29 1.0000 0.0000000
## agePct65up 0.0000 0.0000000
## numbUrban 0.0000 0.0000000
## pctUrban 1.0000 0.0000000
## medIncome 0.0000 0.0000000
## pctWWage 0.0000 0.0000000
## pctWFarmSelf 0.0000 0.0000000
## pctWInvInc 0.0000 1.0000000
## pctWSocSec 1.0000 1.0000000
## pctWPubAsst 1.0000 0.0000000
## pctWRetire 1.0000 1.0000000
## medFamInc 0.0000 0.0000000
## whitePerCap 1.0000 1.0000000
## blackPerCap 0.0000 0.0000000
## indianPerCap 0.0000 0.0000000
## AsianPerCap 0.0000 0.0000000
## OtherPerCap 0.0000 0.0000000
## HispPerCap 0.0000 0.0000000
## NumUnderPov 0.0000 0.0000000
## PctPopUnderPov 0.0000 1.0000000
## PctLess9thGrade 1.0000 1.0000000
## PctBSorMore 0.0000 0.0000000
## PctUnemployed 0.0000 0.0000000
## PctEmploy 0.0000 0.0000000
## PctEmplManu 0.0000 0.0000000
## PctEmplProfServ 0.0000 0.0000000
## PctOccupMgmtProf 0.0000 1.0000000
## MalePctNevMarr 1.0000 1.0000000
## TotalPctDiv 1.0000 1.0000000
## PersPerFam 0.0000 0.0000000
## PctFam2Par 0.0000 0.0000000
## PctWorkMom 0.0000 0.0000000
## PctKidsBornNeverMar 1.0000 1.0000000
## NumImmig 1.0000 1.0000000
## PctImmigRecent 0.0000 0.0000000
## PctRecentImmig 1.0000 1.0000000
## PctSpeakEnglOnly 0.0000 0.0000000
## PctNotSpeakEnglWell 0.0000 0.0000000
## PctLargHouseFam 0.0000 0.0000000
## PersPerOccupHous 1.0000 1.0000000
## PersPerOwnOccHous 0.0000 1.0000000
## PersPerRentOccHous 0.0000 0.0000000
## PctPersOwnOccup 1.0000 0.0000000
## PctPersDenseHous 0.0000 1.0000000
## PctHousLess3BR 0.0000 0.0000000
## MedNumBR 0.0000 0.0000000
## HousVacant 1.0000 1.0000000
## PctHousOccup 1.0000 1.0000000
## PctHousOwnOcc 1.0000 0.0000000
## PctVacantBoarded 0.0000 0.0000000
## PctVacMore6Mos 1.0000 1.0000000
## MedYrHousBuilt 0.0000 0.0000000
## PctHousNoPhone 1.0000 1.0000000
## PctWOFullPlumb 0.0000 0.0000000
## OwnOccLowQuart 1.0000 0.0000000
## OwnOccMedVal 0.0000 0.0000000
## OwnOccHiQuart 0.0000 0.0000000
## RentLowQ 0.0000 0.0000000
## RentMedian 0.0000 0.0000000
## RentHighQ 1.0000 1.0000000
## MedRent 0.0000 0.0000000
## MedRentPctHousInc 1.0000 1.0000000
## MedOwnCostPctInc 0.0000 0.0000000
## MedOwnCostPctIncNoMtg 0.0000 0.0000000
## NumInShelters 0.0000 0.0000000
## NumStreet 1.0000 1.0000000
## PctForeignBorn 1.0000 1.0000000
## PctBornSameState 0.0000 0.0000000
## PctSameHouse85 0.0000 0.0000000
## PctSameCity85 0.0000 0.0000000
## PctSameState85 0.0000 0.0000000
## LandArea 0.0000 0.0000000
## PopDens 1.0000 1.0000000
## PctUsePubTrans 0.0000 0.0000000
## LemasPctOfficDrugUn 0.0000 0.0000000
## agePct22t29 0.0000 1.0000000
## BF 1.0000 0.1858539
## PostProbs 0.0005 0.0005000
## R2 0.5681 0.5673000
## dim 28.0000 28.0000000
## logmarg 715.4921 713.8093380top 5 model
7.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
7.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 22804 models
## post mean post SD post p(B != 0)
## Intercept 1056.78964 11.81393 1.00000
## population -9.26887 32.53918 0.18091
## householdsize -153.53673 70.82293 0.89274
## racepctblack 111.75688 41.84016 0.96108
## racePctWhite 0.45568 20.58773 0.09902
## racePctAsian 1.28270 8.07831 0.10389
## racePctHisp 4.71611 19.91023 0.14769
## agePct12t29 -27.67509 53.94940 0.28871
## agePct65up 10.67873 41.63702 0.16634
## numbUrban 10.66069 32.45154 0.35407
## pctUrban 24.01983 33.58814 0.49945
## medIncome -1.08704 31.48142 0.09063
## pctWWage -6.79032 32.93527 0.12374
## pctWFarmSelf 0.33706 4.26528 0.07145
## pctWInvInc -44.23767 57.46525 0.46062
## pctWSocSec 134.10971 68.16002 0.87530
## pctWPubAsst 34.79750 44.43794 0.46020
## pctWRetire -86.16907 25.70903 0.98374
## medFamInc -6.78459 37.71428 0.11418
## whitePerCap 152.02366 47.28795 0.99026
## blackPerCap 0.16634 4.18880 0.08740
## indianPerCap -0.33078 3.71771 0.09180
## AsianPerCap 0.20321 3.96404 0.07523
## OtherPerCap 6.70692 12.61263 0.28600
## HispPerCap 0.79298 6.33354 0.11045
## NumUnderPov 4.01050 30.84169 0.15994
## PctPopUnderPov 7.11240 31.09752 0.13281
## PctLess9thGrade -65.81723 52.07354 0.70854
## PctBSorMore -6.82790 30.74429 0.13210
## PctUnemployed -1.21354 10.99369 0.09563
## PctEmploy 37.02491 56.99253 0.39009
## PctEmplManu -5.38577 13.29282 0.20842
## PctEmplProfServ -1.17247 9.54212 0.09711
## PctOccupMgmtProf 31.00061 48.20641 0.39280
## MalePctNevMarr 189.56181 49.92505 0.99244
## TotalPctDiv 178.70027 52.13048 0.97465
## PersPerFam -21.52295 54.13092 0.20855
## PctFam2Par -36.66774 69.59367 0.30995
## PctWorkMom -11.36836 22.11326 0.29563
## PctKidsBornNeverMar 56.56951 53.67053 0.61733
## NumImmig 68.66892 59.03795 0.70538
## PctImmigRecent -1.59372 8.45610 0.11919
## PctRecentImmig -90.06808 58.22858 0.79777
## PctSpeakEnglOnly -21.48534 44.02267 0.26757
## PctNotSpeakEnglWell -8.54371 31.98522 0.14905
## PctLargHouseFam -4.61786 22.45401 0.13885
## PersPerOccupHous 385.85465 189.35321 0.92578
## PersPerOwnOccHous -127.65396 127.38742 0.62694
## PersPerRentOccHous -30.96579 60.59847 0.30072
## PctPersOwnOccup -289.75697 369.38546 0.49837
## PctPersDenseHous -30.74458 50.38828 0.35755
## PctHousLess3BR 3.38597 15.73736 0.10954
## MedNumBR -3.73499 11.20557 0.16149
## HousVacant -16.18250 22.09768 0.43073
## PctHousOccup -101.49069 17.92150 0.99917
## PctHousOwnOcc 301.69785 370.88730 0.49741
## PctVacantBoarded 4.96729 13.29818 0.17623
## PctVacMore6Mos -47.00927 22.75144 0.89907
## MedYrHousBuilt 4.39576 14.18112 0.15693
## PctHousNoPhone 59.48536 44.56622 0.73584
## PctWOFullPlumb -0.09972 4.26226 0.07007
## OwnOccLowQuart -3.98060 22.88371 0.12070
## OwnOccMedVal -3.49519 28.51354 0.12010
## OwnOccHiQuart -27.94096 47.65853 0.34339
## RentLowQ -69.76059 69.52005 0.60429
## RentMedian -5.79381 50.62850 0.14430
## RentHighQ -177.09073 106.88745 0.84994
## MedRent 79.19881 111.20196 0.42824
## MedRentPctHousInc 51.50432 28.41898 0.85814
## MedOwnCostPctInc 1.17200 8.23629 0.08788
## MedOwnCostPctIncNoMtg 0.40438 5.28809 0.08498
## NumInShelters 0.67475 6.56027 0.10264
## NumStreet 61.23972 20.02747 0.97489
## PctForeignBorn 135.01400 92.69097 0.77244
## PctBornSameState -3.20281 11.84018 0.13626
## PctSameHouse85 -9.05832 23.04565 0.20324
## PctSameCity85 -2.74580 11.90818 0.12435
## PctSameState85 -1.26656 7.95114 0.09740
## LandArea 1.92571 10.85746 0.12276
## PopDens -31.11407 31.95691 0.57622
## PctUsePubTrans -45.83716 29.57892 0.80152
## LemasPctOfficDrugUn 0.07110 4.16807 0.08598
## agePct22t29 -8.46298 21.23919 0.209627.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
7.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL7.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 3 observations8 larcPerPop
y_name = 'larcPerPop'8.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
8.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.000000e+00 1.000000e+00 1.00000000
## population 0.18555 0.000000e+00 0.000000e+00 1.00000000
## householdsize 0.23120 1.000000e+00 0.000000e+00 0.00000000
## racepctblack 0.16173 0.000000e+00 0.000000e+00 0.00000000
## racePctWhite 0.12005 0.000000e+00 0.000000e+00 0.00000000
## racePctAsian 0.15541 0.000000e+00 0.000000e+00 0.00000000
## racePctHisp 0.14863 0.000000e+00 1.000000e+00 0.00000000
## agePct12t29 0.39296 1.000000e+00 1.000000e+00 0.00000000
## agePct65up 0.32464 0.000000e+00 0.000000e+00 0.00000000
## numbUrban 0.11884 0.000000e+00 0.000000e+00 0.00000000
## pctUrban 0.13001 0.000000e+00 0.000000e+00 0.00000000
## medIncome 0.23166 0.000000e+00 0.000000e+00 0.00000000
## pctWWage 0.68194 1.000000e+00 0.000000e+00 1.00000000
## pctWFarmSelf 0.16497 0.000000e+00 1.000000e+00 0.00000000
## pctWInvInc 0.51194 0.000000e+00 1.000000e+00 0.00000000
## pctWSocSec 0.94747 1.000000e+00 1.000000e+00 1.00000000
## pctWPubAsst 0.34965 1.000000e+00 1.000000e+00 0.00000000
## pctWRetire 0.67101 1.000000e+00 1.000000e+00 1.00000000
## medFamInc 0.37602 0.000000e+00 0.000000e+00 1.00000000
## whitePerCap 0.81810 0.000000e+00 0.000000e+00 1.00000000
## blackPerCap 0.40296 0.000000e+00 1.000000e+00 1.00000000
## indianPerCap 0.09702 0.000000e+00 0.000000e+00 0.00000000
## AsianPerCap 0.25055 1.000000e+00 0.000000e+00 0.00000000
## OtherPerCap 0.63448 0.000000e+00 1.000000e+00 1.00000000
## HispPerCap 0.15612 0.000000e+00 0.000000e+00 0.00000000
## NumUnderPov 0.15801 0.000000e+00 0.000000e+00 0.00000000
## PctPopUnderPov 0.99245 1.000000e+00 1.000000e+00 1.00000000
## PctLess9thGrade 0.91452 1.000000e+00 1.000000e+00 1.00000000
## PctBSorMore 0.11348 0.000000e+00 0.000000e+00 0.00000000
## PctUnemployed 0.15265 0.000000e+00 0.000000e+00 0.00000000
## PctEmploy 0.99129 1.000000e+00 1.000000e+00 1.00000000
## PctEmplManu 0.52188 1.000000e+00 1.000000e+00 0.00000000
## PctEmplProfServ 0.68585 1.000000e+00 1.000000e+00 1.00000000
## PctOccupMgmtProf 0.57549 1.000000e+00 1.000000e+00 1.00000000
## MalePctNevMarr 0.74745 1.000000e+00 0.000000e+00 0.00000000
## TotalPctDiv 0.99890 1.000000e+00 1.000000e+00 1.00000000
## PersPerFam 0.18128 0.000000e+00 0.000000e+00 0.00000000
## PctFam2Par 0.71090 1.000000e+00 1.000000e+00 1.00000000
## PctWorkMom 0.11141 0.000000e+00 0.000000e+00 0.00000000
## PctKidsBornNeverMar 0.19325 0.000000e+00 1.000000e+00 0.00000000
## NumImmig 0.14674 0.000000e+00 0.000000e+00 0.00000000
## PctImmigRecent 0.16265 0.000000e+00 0.000000e+00 0.00000000
## PctRecentImmig 0.92487 1.000000e+00 1.000000e+00 1.00000000
## PctSpeakEnglOnly 0.43800 1.000000e+00 0.000000e+00 1.00000000
## PctNotSpeakEnglWell 0.14099 0.000000e+00 0.000000e+00 0.00000000
## PctLargHouseFam 0.42139 0.000000e+00 0.000000e+00 1.00000000
## PersPerOccupHous 0.26344 0.000000e+00 0.000000e+00 0.00000000
## PersPerOwnOccHous 0.33684 0.000000e+00 0.000000e+00 1.00000000
## PersPerRentOccHous 0.50664 0.000000e+00 0.000000e+00 1.00000000
## PctPersOwnOccup 0.79563 0.000000e+00 1.000000e+00 1.00000000
## PctPersDenseHous 0.12412 0.000000e+00 0.000000e+00 0.00000000
## PctHousLess3BR 0.45678 1.000000e+00 1.000000e+00 1.00000000
## MedNumBR 0.18598 1.000000e+00 0.000000e+00 0.00000000
## HousVacant 0.22934 0.000000e+00 0.000000e+00 0.00000000
## PctHousOccup 0.24523 0.000000e+00 0.000000e+00 0.00000000
## PctHousOwnOcc 0.71144 1.000000e+00 1.000000e+00 0.00000000
## PctVacantBoarded 0.26650 0.000000e+00 1.000000e+00 0.00000000
## PctVacMore6Mos 0.45058 1.000000e+00 0.000000e+00 0.00000000
## MedYrHousBuilt 0.87986 1.000000e+00 1.000000e+00 1.00000000
## PctHousNoPhone 0.23198 1.000000e+00 0.000000e+00 0.00000000
## PctWOFullPlumb 0.09553 0.000000e+00 0.000000e+00 0.00000000
## OwnOccLowQuart 0.18770 0.000000e+00 0.000000e+00 0.00000000
## OwnOccMedVal 0.33140 1.000000e+00 0.000000e+00 0.00000000
## OwnOccHiQuart 0.28415 0.000000e+00 0.000000e+00 0.00000000
## RentLowQ 0.27120 0.000000e+00 0.000000e+00 0.00000000
## RentMedian 0.35819 0.000000e+00 0.000000e+00 1.00000000
## RentHighQ 0.21633 1.000000e+00 0.000000e+00 0.00000000
## MedRent 0.30726 0.000000e+00 1.000000e+00 1.00000000
## MedRentPctHousInc 0.24676 0.000000e+00 0.000000e+00 0.00000000
## MedOwnCostPctInc 0.91878 1.000000e+00 1.000000e+00 1.00000000
## MedOwnCostPctIncNoMtg 0.15125 0.000000e+00 0.000000e+00 0.00000000
## NumInShelters 0.82854 1.000000e+00 1.000000e+00 1.00000000
## NumStreet 0.99240 1.000000e+00 1.000000e+00 1.00000000
## PctForeignBorn 0.88492 1.000000e+00 1.000000e+00 1.00000000
## PctBornSameState 0.53924 1.000000e+00 0.000000e+00 1.00000000
## PctSameHouse85 0.11558 0.000000e+00 0.000000e+00 0.00000000
## PctSameCity85 0.14933 0.000000e+00 0.000000e+00 0.00000000
## PctSameState85 0.21360 0.000000e+00 0.000000e+00 0.00000000
## LandArea 0.86035 1.000000e+00 1.000000e+00 0.00000000
## PopDens 0.99985 1.000000e+00 1.000000e+00 1.00000000
## PctUsePubTrans 0.10048 0.000000e+00 0.000000e+00 0.00000000
## LemasPctOfficDrugUn 0.43883 0.000000e+00 0.000000e+00 0.00000000
## agePct22t29 0.15746 0.000000e+00 1.000000e+00 0.00000000
## BF NA 1.239982e-04 7.917376e-04 0.07980822
## PostProbs NA 4.000000e-04 3.000000e-04 0.00030000
## R2 NA 4.672000e-01 4.669000e-01 0.46820000
## dim NA 3.400000e+01 3.300000e+01 32.00000000
## logmarg NA 5.046437e+02 5.064976e+02 511.11077649
## model 4 model 5
## Intercept 1.000000e+00 1.0000
## population 0.000000e+00 0.0000
## householdsize 0.000000e+00 0.0000
## racepctblack 0.000000e+00 1.0000
## racePctWhite 0.000000e+00 0.0000
## racePctAsian 0.000000e+00 0.0000
## racePctHisp 0.000000e+00 0.0000
## agePct12t29 0.000000e+00 1.0000
## agePct65up 1.000000e+00 0.0000
## numbUrban 0.000000e+00 0.0000
## pctUrban 0.000000e+00 0.0000
## medIncome 1.000000e+00 0.0000
## pctWWage 0.000000e+00 1.0000
## pctWFarmSelf 0.000000e+00 0.0000
## pctWInvInc 0.000000e+00 0.0000
## pctWSocSec 1.000000e+00 1.0000
## pctWPubAsst 0.000000e+00 0.0000
## pctWRetire 0.000000e+00 0.0000
## medFamInc 1.000000e+00 1.0000
## whitePerCap 1.000000e+00 1.0000
## blackPerCap 0.000000e+00 0.0000
## indianPerCap 0.000000e+00 0.0000
## AsianPerCap 0.000000e+00 0.0000
## OtherPerCap 1.000000e+00 1.0000
## HispPerCap 0.000000e+00 0.0000
## NumUnderPov 0.000000e+00 0.0000
## PctPopUnderPov 1.000000e+00 1.0000
## PctLess9thGrade 1.000000e+00 1.0000
## PctBSorMore 0.000000e+00 0.0000
## PctUnemployed 0.000000e+00 0.0000
## PctEmploy 1.000000e+00 1.0000
## PctEmplManu 0.000000e+00 0.0000
## PctEmplProfServ 0.000000e+00 1.0000
## PctOccupMgmtProf 0.000000e+00 1.0000
## MalePctNevMarr 1.000000e+00 1.0000
## TotalPctDiv 1.000000e+00 1.0000
## PersPerFam 0.000000e+00 0.0000
## PctFam2Par 1.000000e+00 1.0000
## PctWorkMom 0.000000e+00 0.0000
## PctKidsBornNeverMar 0.000000e+00 0.0000
## NumImmig 0.000000e+00 0.0000
## PctImmigRecent 0.000000e+00 1.0000
## PctRecentImmig 0.000000e+00 1.0000
## PctSpeakEnglOnly 1.000000e+00 0.0000
## PctNotSpeakEnglWell 0.000000e+00 0.0000
## PctLargHouseFam 0.000000e+00 0.0000
## PersPerOccupHous 0.000000e+00 0.0000
## PersPerOwnOccHous 1.000000e+00 1.0000
## PersPerRentOccHous 1.000000e+00 1.0000
## PctPersOwnOccup 1.000000e+00 1.0000
## PctPersDenseHous 1.000000e+00 0.0000
## PctHousLess3BR 0.000000e+00 0.0000
## MedNumBR 0.000000e+00 0.0000
## HousVacant 0.000000e+00 0.0000
## PctHousOccup 0.000000e+00 0.0000
## PctHousOwnOcc 1.000000e+00 1.0000
## PctVacantBoarded 1.000000e+00 0.0000
## PctVacMore6Mos 0.000000e+00 0.0000
## MedYrHousBuilt 1.000000e+00 1.0000
## PctHousNoPhone 1.000000e+00 0.0000
## PctWOFullPlumb 0.000000e+00 0.0000
## OwnOccLowQuart 0.000000e+00 0.0000
## OwnOccMedVal 1.000000e+00 0.0000
## OwnOccHiQuart 0.000000e+00 1.0000
## RentLowQ 0.000000e+00 0.0000
## RentMedian 0.000000e+00 1.0000
## RentHighQ 0.000000e+00 0.0000
## MedRent 0.000000e+00 0.0000
## MedRentPctHousInc 0.000000e+00 0.0000
## MedOwnCostPctInc 1.000000e+00 1.0000
## MedOwnCostPctIncNoMtg 0.000000e+00 0.0000
## NumInShelters 1.000000e+00 1.0000
## NumStreet 1.000000e+00 1.0000
## PctForeignBorn 0.000000e+00 1.0000
## PctBornSameState 1.000000e+00 1.0000
## PctSameHouse85 0.000000e+00 0.0000
## PctSameCity85 0.000000e+00 1.0000
## PctSameState85 0.000000e+00 0.0000
## LandArea 1.000000e+00 1.0000
## PopDens 1.000000e+00 1.0000
## PctUsePubTrans 0.000000e+00 0.0000
## LemasPctOfficDrugUn 1.000000e+00 0.0000
## agePct22t29 0.000000e+00 0.0000
## BF 7.543113e-03 1.0000
## PostProbs 3.000000e-04 0.0003
## R2 4.642000e-01 0.4710
## dim 3.000000e+01 33.0000
## logmarg 5.087518e+02 513.6389top 5 model
8.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
8.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 27030 models
## post mean post SD post p(B != 0)
## Intercept 3.370e+03 3.304e+01 1.000e+00
## population -1.642e+01 8.129e+01 1.855e-01
## householdsize -4.031e+01 1.061e+02 2.312e-01
## racepctblack -8.996e+00 4.811e+01 1.617e-01
## racePctWhite 5.078e+00 3.959e+01 1.201e-01
## racePctAsian 9.268e+00 3.182e+01 1.554e-01
## racePctHisp -1.130e+00 5.453e+01 1.486e-01
## agePct12t29 -1.097e+02 1.753e+02 3.930e-01
## agePct65up 1.127e+02 2.041e+02 3.246e-01
## numbUrban -1.524e+01 9.369e+01 1.188e-01
## pctUrban 1.840e+01 9.212e+01 1.300e-01
## medIncome -6.458e+01 2.006e+02 2.317e-01
## pctWWage 3.050e+02 2.550e+02 6.819e-01
## pctWFarmSelf -8.043e+00 2.550e+01 1.650e-01
## pctWInvInc 1.277e+02 1.518e+02 5.119e-01
## pctWSocSec 6.629e+02 2.504e+02 9.475e-01
## pctWPubAsst -6.484e+01 1.086e+02 3.497e-01
## pctWRetire -1.095e+02 9.526e+01 6.710e-01
## medFamInc -1.757e+02 2.771e+02 3.760e-01
## whitePerCap 3.380e+02 2.222e+02 8.181e-01
## blackPerCap -3.085e+01 4.508e+01 4.030e-01
## indianPerCap -9.171e-01 1.062e+01 9.702e-02
## AsianPerCap -1.485e+01 3.253e+01 2.505e-01
## OtherPerCap 5.394e+01 4.989e+01 6.345e-01
## HispPerCap 8.777e+00 2.886e+01 1.561e-01
## NumUnderPov 1.540e+01 9.406e+01 1.580e-01
## PctPopUnderPov 6.345e+02 1.674e+02 9.925e-01
## PctLess9thGrade -2.558e+02 1.215e+02 9.145e-01
## PctBSorMore -8.392e+00 6.842e+01 1.135e-01
## PctUnemployed -1.382e+01 4.820e+01 1.527e-01
## PctEmploy 4.887e+02 1.480e+02 9.913e-01
## PctEmplManu -6.231e+01 7.213e+01 5.219e-01
## PctEmplProfServ -1.430e+02 1.227e+02 6.858e-01
## PctOccupMgmtProf 1.693e+02 1.784e+02 5.755e-01
## MalePctNevMarr 2.551e+02 2.007e+02 7.474e-01
## TotalPctDiv 4.949e+02 1.383e+02 9.989e-01
## PersPerFam 7.683e+00 1.094e+02 1.813e-01
## PctFam2Par -3.215e+02 2.572e+02 7.109e-01
## PctWorkMom -2.906e+00 2.192e+01 1.114e-01
## PctKidsBornNeverMar 2.333e+01 6.974e+01 1.933e-01
## NumImmig 1.447e+01 6.176e+01 1.467e-01
## PctImmigRecent 8.598e+00 2.875e+01 1.626e-01
## PctRecentImmig -3.280e+02 1.463e+02 9.249e-01
## PctSpeakEnglOnly -1.095e+02 1.550e+02 4.380e-01
## PctNotSpeakEnglWell 1.632e+01 7.384e+01 1.410e-01
## PctLargHouseFam 9.588e+01 1.424e+02 4.214e-01
## PersPerOccupHous 9.228e+01 2.262e+02 2.634e-01
## PersPerOwnOccHous 6.454e+01 2.337e+02 3.368e-01
## PersPerRentOccHous -1.884e+02 2.427e+02 5.066e-01
## PctPersOwnOccup -1.261e+03 1.134e+03 7.956e-01
## PctPersDenseHous -3.917e+00 5.156e+01 1.241e-01
## PctHousLess3BR -9.615e+01 1.282e+02 4.568e-01
## MedNumBR -1.346e+01 3.809e+01 1.860e-01
## HousVacant -1.571e+01 3.724e+01 2.293e-01
## PctHousOccup -1.866e+01 4.111e+01 2.452e-01
## PctHousOwnOcc 1.025e+03 1.057e+03 7.114e-01
## PctVacantBoarded -2.089e+01 4.342e+01 2.665e-01
## PctVacMore6Mos -4.555e+01 6.091e+01 4.506e-01
## MedYrHousBuilt 1.869e+02 9.809e+01 8.799e-01
## PctHousNoPhone 2.976e+01 6.994e+01 2.320e-01
## PctWOFullPlumb -1.057e+00 1.430e+01 9.553e-02
## OwnOccLowQuart -2.921e+01 1.021e+02 1.877e-01
## OwnOccMedVal -8.534e+01 1.549e+02 3.314e-01
## OwnOccHiQuart -6.438e+01 1.294e+02 2.842e-01
## RentLowQ -5.426e+01 1.109e+02 2.712e-01
## RentMedian -1.106e+02 1.863e+02 3.582e-01
## RentHighQ -5.105e+01 1.311e+02 2.163e-01
## MedRent -8.076e+01 1.586e+02 3.073e-01
## MedRentPctHousInc -2.225e+01 4.931e+01 2.468e-01
## MedOwnCostPctInc -1.858e+02 8.388e+01 9.188e-01
## MedOwnCostPctIncNoMtg 7.900e+00 2.681e+01 1.512e-01
## NumInShelters 1.219e+02 7.326e+01 8.285e-01
## NumStreet 1.879e+02 5.306e+01 9.924e-01
## PctForeignBorn 4.553e+02 2.293e+02 8.849e-01
## PctBornSameState -7.269e+01 8.160e+01 5.392e-01
## PctSameHouse85 4.929e+00 3.984e+01 1.156e-01
## PctSameCity85 7.959e+00 3.712e+01 1.493e-01
## PctSameState85 -1.704e+01 4.840e+01 2.136e-01
## LandArea -1.604e+02 8.953e+01 8.603e-01
## PopDens -3.907e+02 7.301e+01 9.999e-01
## PctUsePubTrans 3.712e-01 1.832e+01 1.005e-01
## LemasPctOfficDrugUn 3.531e+01 4.777e+01 4.388e-01
## agePct22t29 -1.557e+01 5.172e+01 1.575e-018.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
8.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL8.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 3 observations9 autoTheftPerPop
y_name = 'autoTheftPerPop'9.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
9.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.000000e+00 1.000000e+00 1.0000
## population 0.45658 0.000000e+00 0.000000e+00 0.0000
## householdsize 0.54852 0.000000e+00 0.000000e+00 0.0000
## racepctblack 0.17508 0.000000e+00 0.000000e+00 0.0000
## racePctWhite 0.92562 1.000000e+00 1.000000e+00 1.0000
## racePctAsian 0.94482 1.000000e+00 1.000000e+00 1.0000
## racePctHisp 0.19471 0.000000e+00 0.000000e+00 1.0000
## agePct12t29 0.26319 0.000000e+00 1.000000e+00 0.0000
## agePct65up 0.13078 0.000000e+00 0.000000e+00 0.0000
## numbUrban 0.25717 0.000000e+00 0.000000e+00 0.0000
## pctUrban 0.27850 1.000000e+00 0.000000e+00 0.0000
## medIncome 0.67072 1.000000e+00 0.000000e+00 1.0000
## pctWWage 0.09838 0.000000e+00 0.000000e+00 0.0000
## pctWFarmSelf 0.49571 0.000000e+00 0.000000e+00 0.0000
## pctWInvInc 0.96817 1.000000e+00 1.000000e+00 1.0000
## pctWSocSec 0.99041 1.000000e+00 1.000000e+00 1.0000
## pctWPubAsst 0.13800 1.000000e+00 0.000000e+00 0.0000
## pctWRetire 0.71547 1.000000e+00 1.000000e+00 0.0000
## medFamInc 0.25732 0.000000e+00 1.000000e+00 0.0000
## whitePerCap 0.13733 0.000000e+00 0.000000e+00 0.0000
## blackPerCap 0.11752 0.000000e+00 0.000000e+00 0.0000
## indianPerCap 0.08756 0.000000e+00 0.000000e+00 0.0000
## AsianPerCap 0.07559 0.000000e+00 0.000000e+00 0.0000
## OtherPerCap 0.08115 0.000000e+00 0.000000e+00 0.0000
## HispPerCap 0.12514 0.000000e+00 0.000000e+00 0.0000
## NumUnderPov 0.26766 0.000000e+00 1.000000e+00 0.0000
## PctPopUnderPov 0.49839 0.000000e+00 0.000000e+00 0.0000
## PctLess9thGrade 0.90519 1.000000e+00 1.000000e+00 1.0000
## PctBSorMore 0.27801 0.000000e+00 1.000000e+00 0.0000
## PctUnemployed 0.11700 0.000000e+00 0.000000e+00 0.0000
## PctEmploy 0.67665 1.000000e+00 1.000000e+00 1.0000
## PctEmplManu 0.09823 0.000000e+00 0.000000e+00 0.0000
## PctEmplProfServ 0.09062 0.000000e+00 0.000000e+00 0.0000
## PctOccupMgmtProf 0.28397 0.000000e+00 1.000000e+00 0.0000
## MalePctNevMarr 0.99884 1.000000e+00 1.000000e+00 1.0000
## TotalPctDiv 0.99939 1.000000e+00 1.000000e+00 1.0000
## PersPerFam 0.26381 0.000000e+00 1.000000e+00 0.0000
## PctFam2Par 0.16131 0.000000e+00 0.000000e+00 0.0000
## PctWorkMom 0.99920 1.000000e+00 1.000000e+00 1.0000
## PctKidsBornNeverMar 0.12426 0.000000e+00 0.000000e+00 0.0000
## NumImmig 0.44576 1.000000e+00 0.000000e+00 1.0000
## PctImmigRecent 0.11447 0.000000e+00 0.000000e+00 0.0000
## PctRecentImmig 0.93874 1.000000e+00 1.000000e+00 1.0000
## PctSpeakEnglOnly 0.13118 1.000000e+00 0.000000e+00 0.0000
## PctNotSpeakEnglWell 0.23462 0.000000e+00 0.000000e+00 0.0000
## PctLargHouseFam 0.84617 1.000000e+00 0.000000e+00 1.0000
## PersPerOccupHous 0.62624 1.000000e+00 1.000000e+00 1.0000
## PersPerOwnOccHous 0.99860 1.000000e+00 1.000000e+00 1.0000
## PersPerRentOccHous 0.80548 1.000000e+00 1.000000e+00 1.0000
## PctPersOwnOccup 0.99821 1.000000e+00 1.000000e+00 1.0000
## PctPersDenseHous 0.28365 0.000000e+00 0.000000e+00 1.0000
## PctHousLess3BR 0.91887 1.000000e+00 1.000000e+00 1.0000
## MedNumBR 0.12216 1.000000e+00 0.000000e+00 0.0000
## HousVacant 0.08147 0.000000e+00 0.000000e+00 0.0000
## PctHousOccup 0.30329 0.000000e+00 0.000000e+00 0.0000
## PctHousOwnOcc 0.99871 1.000000e+00 1.000000e+00 1.0000
## PctVacantBoarded 0.94362 1.000000e+00 1.000000e+00 1.0000
## PctVacMore6Mos 0.97472 1.000000e+00 1.000000e+00 1.0000
## MedYrHousBuilt 0.09221 0.000000e+00 0.000000e+00 0.0000
## PctHousNoPhone 0.85286 1.000000e+00 1.000000e+00 1.0000
## PctWOFullPlumb 0.08341 0.000000e+00 0.000000e+00 0.0000
## OwnOccLowQuart 0.76448 1.000000e+00 1.000000e+00 1.0000
## OwnOccMedVal 0.27768 1.000000e+00 0.000000e+00 0.0000
## OwnOccHiQuart 0.40580 1.000000e+00 1.000000e+00 0.0000
## RentLowQ 0.11556 0.000000e+00 0.000000e+00 0.0000
## RentMedian 0.11174 0.000000e+00 0.000000e+00 0.0000
## RentHighQ 0.24823 0.000000e+00 1.000000e+00 0.0000
## MedRent 0.10197 0.000000e+00 0.000000e+00 0.0000
## MedRentPctHousInc 0.16399 0.000000e+00 0.000000e+00 0.0000
## MedOwnCostPctInc 0.12654 0.000000e+00 0.000000e+00 0.0000
## MedOwnCostPctIncNoMtg 0.95371 1.000000e+00 1.000000e+00 1.0000
## NumInShelters 0.30263 0.000000e+00 1.000000e+00 0.0000
## NumStreet 0.99788 1.000000e+00 1.000000e+00 1.0000
## PctForeignBorn 0.99942 1.000000e+00 1.000000e+00 1.0000
## PctBornSameState 0.10312 0.000000e+00 0.000000e+00 0.0000
## PctSameHouse85 0.22440 1.000000e+00 0.000000e+00 0.0000
## PctSameCity85 0.64611 0.000000e+00 1.000000e+00 1.0000
## PctSameState85 0.11745 0.000000e+00 0.000000e+00 0.0000
## LandArea 0.11988 0.000000e+00 0.000000e+00 0.0000
## PopDens 0.29345 0.000000e+00 0.000000e+00 0.0000
## PctUsePubTrans 0.82459 0.000000e+00 0.000000e+00 1.0000
## LemasPctOfficDrugUn 0.21160 0.000000e+00 0.000000e+00 0.0000
## agePct22t29 0.13027 0.000000e+00 0.000000e+00 1.0000
## BF NA 4.890769e-04 5.454184e-03 1.0000
## PostProbs NA 6.000000e-04 6.000000e-04 0.0006
## R2 NA 5.914000e-01 5.925000e-01 0.5915
## dim NA 3.500000e+01 3.500000e+01 32.0000
## logmarg NA 7.499679e+02 7.523795e+02 757.5909
## model 4 model 5
## Intercept 1.000000e+00 1.000000e+00
## population 0.000000e+00 0.000000e+00
## householdsize 0.000000e+00 0.000000e+00
## racepctblack 1.000000e+00 0.000000e+00
## racePctWhite 1.000000e+00 1.000000e+00
## racePctAsian 1.000000e+00 1.000000e+00
## racePctHisp 0.000000e+00 1.000000e+00
## agePct12t29 0.000000e+00 0.000000e+00
## agePct65up 0.000000e+00 0.000000e+00
## numbUrban 0.000000e+00 0.000000e+00
## pctUrban 1.000000e+00 0.000000e+00
## medIncome 1.000000e+00 0.000000e+00
## pctWWage 0.000000e+00 0.000000e+00
## pctWFarmSelf 0.000000e+00 0.000000e+00
## pctWInvInc 1.000000e+00 1.000000e+00
## pctWSocSec 1.000000e+00 1.000000e+00
## pctWPubAsst 0.000000e+00 0.000000e+00
## pctWRetire 1.000000e+00 1.000000e+00
## medFamInc 0.000000e+00 1.000000e+00
## whitePerCap 0.000000e+00 0.000000e+00
## blackPerCap 0.000000e+00 0.000000e+00
## indianPerCap 0.000000e+00 0.000000e+00
## AsianPerCap 0.000000e+00 0.000000e+00
## OtherPerCap 0.000000e+00 0.000000e+00
## HispPerCap 0.000000e+00 0.000000e+00
## NumUnderPov 1.000000e+00 0.000000e+00
## PctPopUnderPov 0.000000e+00 0.000000e+00
## PctLess9thGrade 1.000000e+00 0.000000e+00
## PctBSorMore 1.000000e+00 0.000000e+00
## PctUnemployed 0.000000e+00 0.000000e+00
## PctEmploy 1.000000e+00 1.000000e+00
## PctEmplManu 0.000000e+00 0.000000e+00
## PctEmplProfServ 0.000000e+00 0.000000e+00
## PctOccupMgmtProf 0.000000e+00 0.000000e+00
## MalePctNevMarr 1.000000e+00 1.000000e+00
## TotalPctDiv 1.000000e+00 1.000000e+00
## PersPerFam 0.000000e+00 0.000000e+00
## PctFam2Par 0.000000e+00 1.000000e+00
## PctWorkMom 1.000000e+00 1.000000e+00
## PctKidsBornNeverMar 0.000000e+00 0.000000e+00
## NumImmig 1.000000e+00 1.000000e+00
## PctImmigRecent 0.000000e+00 0.000000e+00
## PctRecentImmig 1.000000e+00 1.000000e+00
## PctSpeakEnglOnly 0.000000e+00 0.000000e+00
## PctNotSpeakEnglWell 0.000000e+00 0.000000e+00
## PctLargHouseFam 1.000000e+00 1.000000e+00
## PersPerOccupHous 1.000000e+00 1.000000e+00
## PersPerOwnOccHous 1.000000e+00 1.000000e+00
## PersPerRentOccHous 1.000000e+00 1.000000e+00
## PctPersOwnOccup 1.000000e+00 1.000000e+00
## PctPersDenseHous 0.000000e+00 0.000000e+00
## PctHousLess3BR 1.000000e+00 1.000000e+00
## MedNumBR 0.000000e+00 0.000000e+00
## HousVacant 0.000000e+00 1.000000e+00
## PctHousOccup 0.000000e+00 1.000000e+00
## PctHousOwnOcc 1.000000e+00 1.000000e+00
## PctVacantBoarded 1.000000e+00 1.000000e+00
## PctVacMore6Mos 1.000000e+00 1.000000e+00
## MedYrHousBuilt 0.000000e+00 0.000000e+00
## PctHousNoPhone 1.000000e+00 1.000000e+00
## PctWOFullPlumb 0.000000e+00 0.000000e+00
## OwnOccLowQuart 1.000000e+00 1.000000e+00
## OwnOccMedVal 0.000000e+00 0.000000e+00
## OwnOccHiQuart 0.000000e+00 0.000000e+00
## RentLowQ 0.000000e+00 0.000000e+00
## RentMedian 0.000000e+00 0.000000e+00
## RentHighQ 1.000000e+00 0.000000e+00
## MedRent 0.000000e+00 0.000000e+00
## MedRentPctHousInc 0.000000e+00 0.000000e+00
## MedOwnCostPctInc 0.000000e+00 0.000000e+00
## MedOwnCostPctIncNoMtg 1.000000e+00 1.000000e+00
## NumInShelters 1.000000e+00 1.000000e+00
## NumStreet 1.000000e+00 1.000000e+00
## PctForeignBorn 1.000000e+00 1.000000e+00
## PctBornSameState 0.000000e+00 0.000000e+00
## PctSameHouse85 0.000000e+00 0.000000e+00
## PctSameCity85 1.000000e+00 1.000000e+00
## PctSameState85 0.000000e+00 0.000000e+00
## LandArea 0.000000e+00 0.000000e+00
## PopDens 0.000000e+00 0.000000e+00
## PctUsePubTrans 1.000000e+00 1.000000e+00
## LemasPctOfficDrugUn 0.000000e+00 0.000000e+00
## agePct22t29 0.000000e+00 0.000000e+00
## BF 5.690978e-03 2.486134e-03
## PostProbs 6.000000e-04 5.000000e-04
## R2 5.936000e-01 5.910000e-01
## dim 3.600000e+01 3.400000e+01
## logmarg 7.524220e+02 7.515938e+02top 5 model
9.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
9.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 19810 models
## post mean post SD post p(B != 0)
## Intercept 483.27783 7.49098 1.00000
## population 20.45982 27.16575 0.45658
## householdsize -47.27980 50.93074 0.54852
## racepctblack 10.17035 30.30249 0.17508
## racePctWhite -120.37727 41.06337 0.92562
## racePctAsian -50.95543 18.52333 0.94482
## racePctHisp -6.14658 17.16623 0.19471
## agePct12t29 -14.18694 29.26382 0.26319
## agePct65up 4.80909 21.70564 0.13078
## numbUrban 5.44792 13.17481 0.25717
## pctUrban 5.72908 12.68340 0.27850
## medIncome 84.31681 71.25286 0.67072
## pctWWage -1.79944 13.74895 0.09838
## pctWFarmSelf 10.50581 12.57979 0.49571
## pctWInvInc -95.88972 34.41879 0.96817
## pctWSocSec 148.91534 36.81554 0.99041
## pctWPubAsst 3.12970 11.53596 0.13800
## pctWRetire -29.66026 23.44896 0.71547
## medFamInc 19.97747 50.00781 0.25732
## whitePerCap 3.75081 16.45259 0.13733
## blackPerCap -0.73142 3.68434 0.11752
## indianPerCap -0.27464 2.38245 0.08756
## AsianPerCap -0.08687 2.50665 0.07559
## OtherPerCap 0.27128 2.47941 0.08115
## HispPerCap 0.90848 4.50890 0.12514
## NumUnderPov 12.25371 28.83041 0.26766
## PctPopUnderPov -45.10923 54.63946 0.49839
## PctLess9thGrade -62.06848 28.87602 0.90519
## PctBSorMore -19.42713 40.29858 0.27801
## PctUnemployed 1.85347 8.87726 0.11700
## PctEmploy 60.35750 49.50913 0.67665
## PctEmplManu 0.38817 3.75740 0.09823
## PctEmplProfServ -0.32204 4.82373 0.09062
## PctOccupMgmtProf 16.64815 34.13959 0.28397
## MalePctNevMarr 163.33069 32.39099 0.99884
## TotalPctDiv 129.39465 25.66146 0.99939
## PersPerFam -27.87587 57.71270 0.26381
## PctFam2Par 7.44426 23.84257 0.16131
## PctWorkMom -63.95244 14.06450 0.99920
## PctKidsBornNeverMar 2.76186 12.26678 0.12426
## NumImmig 26.74120 34.95048 0.44576
## PctImmigRecent -0.46291 4.34993 0.11447
## PctRecentImmig -71.89477 29.31873 0.93874
## PctSpeakEnglOnly -0.59736 15.09367 0.13118
## PctNotSpeakEnglWell -13.12669 30.05745 0.23462
## PctLargHouseFam -84.33084 47.03689 0.84617
## PersPerOccupHous -163.82161 152.09552 0.62624
## PersPerOwnOccHous 368.38379 93.16978 0.99860
## PersPerRentOccHous -85.18688 54.22476 0.80548
## PctPersOwnOccup -900.85344 262.28496 0.99821
## PctPersDenseHous 18.55940 37.23479 0.28365
## PctHousLess3BR 69.22595 30.42090 0.91887
## MedNumBR -1.01933 5.44166 0.12216
## HousVacant 0.17626 3.28382 0.08147
## PctHousOccup -5.46652 10.19620 0.30329
## PctHousOwnOcc 926.87289 257.12278 0.99871
## PctVacantBoarded 35.41376 13.98042 0.94362
## PctVacMore6Mos -38.42935 12.91190 0.97472
## MedYrHousBuilt 0.62707 5.37681 0.09221
## PctHousNoPhone -52.11285 28.96249 0.85286
## PctWOFullPlumb -0.31396 3.10348 0.08341
## OwnOccLowQuart -100.38977 77.15622 0.76448
## OwnOccMedVal 15.02399 93.68534 0.27768
## OwnOccHiQuart -39.53362 59.38814 0.40580
## RentLowQ -1.53653 10.23434 0.11556
## RentMedian -0.35983 15.99421 0.11174
## RentHighQ -12.54486 28.70553 0.24823
## MedRent 0.88864 15.62696 0.10197
## MedRentPctHousInc -2.37696 7.65239 0.16399
## MedOwnCostPctInc -1.61377 7.33557 0.12654
## MedOwnCostPctIncNoMtg -33.13786 12.96531 0.95371
## NumInShelters -6.60329 11.99820 0.30263
## NumStreet 65.41308 11.43249 0.99788
## PctForeignBorn 237.73700 42.49077 0.99942
## PctBornSameState -0.34411 5.33192 0.10312
## PctSameHouse85 7.16135 17.63864 0.22440
## PctSameCity85 26.33473 23.51942 0.64611
## PctSameState85 0.80950 5.98529 0.11745
## LandArea 0.29037 6.35890 0.11988
## PopDens -7.39092 14.09756 0.29345
## PctUsePubTrans 27.97856 17.36209 0.82459
## LemasPctOfficDrugUn 2.91398 6.97319 0.21160
## agePct22t29 -2.31836 9.01129 0.130279.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
9.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL9.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 3 observations10 arsonsPerPop
y_name = 'arsonsPerPop'10.1 Model fit
f = paste(y_name, " ~ . -murdPerPop -rapesPerPop -robbbPerPop -assaultPerPop -burglPerPop -larcPerPop -autoTheftPerPop -arsonsPerPop")
fit.gprior = bas.lm(f,
data = data,
method = "MCMC", # better than default "BAS"
# for large p
prior = "ZS-null", # default
# "JZS" also can use
modelprior = uniform(),
include.always = ~1,
MCMC.iterations = 100000)## Warning in bas.lm(f, data = data, method = "MCMC", prior = "ZS-null", modelprior
## = uniform(), : dropping 313 rows due to missing dataplot(fit.gprior, ask = F)
10.2 model result
summary(fit.gprior)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000 1.00000000 1.0000000 1.000000
## population 0.40424 1.00000000 0.0000000 0.000000
## householdsize 0.11063 0.00000000 0.0000000 1.000000
## racepctblack 0.30800 0.00000000 1.0000000 0.000000
## racePctWhite 0.38524 0.00000000 1.0000000 0.000000
## racePctAsian 0.16385 0.00000000 0.0000000 0.000000
## racePctHisp 0.19265 0.00000000 0.0000000 0.000000
## agePct12t29 0.14444 0.00000000 0.0000000 0.000000
## agePct65up 0.12009 0.00000000 0.0000000 0.000000
## numbUrban 0.48569 1.00000000 1.0000000 1.000000
## pctUrban 0.45996 0.00000000 0.0000000 0.000000
## medIncome 0.12839 0.00000000 0.0000000 0.000000
## pctWWage 0.21667 0.00000000 0.0000000 0.000000
## pctWFarmSelf 0.09340 1.00000000 0.0000000 0.000000
## pctWInvInc 0.29442 0.00000000 0.0000000 0.000000
## pctWSocSec 0.13551 0.00000000 0.0000000 0.000000
## pctWPubAsst 0.96497 1.00000000 1.0000000 1.000000
## pctWRetire 0.08704 1.00000000 0.0000000 0.000000
## medFamInc 0.14752 0.00000000 0.0000000 0.000000
## whitePerCap 0.31434 0.00000000 0.0000000 0.000000
## blackPerCap 0.10668 0.00000000 0.0000000 0.000000
## indianPerCap 0.07877 0.00000000 0.0000000 0.000000
## AsianPerCap 0.17188 0.00000000 0.0000000 0.000000
## OtherPerCap 0.33760 0.00000000 0.0000000 0.000000
## HispPerCap 0.08407 0.00000000 0.0000000 0.000000
## NumUnderPov 0.14618 0.00000000 0.0000000 0.000000
## PctPopUnderPov 0.35704 0.00000000 1.0000000 0.000000
## PctLess9thGrade 0.69271 1.00000000 0.0000000 0.000000
## PctBSorMore 0.12990 0.00000000 0.0000000 0.000000
## PctUnemployed 0.11484 0.00000000 0.0000000 0.000000
## PctEmploy 0.12119 0.00000000 0.0000000 0.000000
## PctEmplManu 0.45668 1.00000000 0.0000000 0.000000
## PctEmplProfServ 0.09596 0.00000000 0.0000000 0.000000
## PctOccupMgmtProf 0.15517 0.00000000 0.0000000 0.000000
## MalePctNevMarr 0.19976 0.00000000 0.0000000 0.000000
## TotalPctDiv 0.99203 1.00000000 1.0000000 1.000000
## PersPerFam 0.11076 0.00000000 0.0000000 0.000000
## PctFam2Par 0.16089 0.00000000 0.0000000 1.000000
## PctWorkMom 0.12742 0.00000000 0.0000000 0.000000
## PctKidsBornNeverMar 0.13533 0.00000000 0.0000000 0.000000
## NumImmig 0.68463 0.00000000 1.0000000 1.000000
## PctImmigRecent 0.08400 0.00000000 0.0000000 0.000000
## PctRecentImmig 0.11577 0.00000000 0.0000000 0.000000
## PctSpeakEnglOnly 0.13692 0.00000000 1.0000000 0.000000
## PctNotSpeakEnglWell 0.16348 0.00000000 0.0000000 0.000000
## PctLargHouseFam 0.11041 1.00000000 0.0000000 0.000000
## PersPerOccupHous 0.15867 0.00000000 0.0000000 0.000000
## PersPerOwnOccHous 0.11844 0.00000000 1.0000000 0.000000
## PersPerRentOccHous 0.15993 0.00000000 1.0000000 0.000000
## PctPersOwnOccup 0.10484 0.00000000 0.0000000 0.000000
## PctPersDenseHous 0.14153 0.00000000 0.0000000 0.000000
## PctHousLess3BR 0.18842 0.00000000 0.0000000 0.000000
## MedNumBR 0.20651 0.00000000 0.0000000 0.000000
## HousVacant 0.10180 0.00000000 0.0000000 0.000000
## PctHousOccup 0.09873 0.00000000 0.0000000 0.000000
## PctHousOwnOcc 0.09108 0.00000000 0.0000000 0.000000
## PctVacantBoarded 0.99926 1.00000000 1.0000000 1.000000
## PctVacMore6Mos 0.11226 0.00000000 0.0000000 0.000000
## MedYrHousBuilt 0.10893 0.00000000 0.0000000 0.000000
## PctHousNoPhone 0.22986 1.00000000 0.0000000 0.000000
## PctWOFullPlumb 0.23707 0.00000000 0.0000000 1.000000
## OwnOccLowQuart 0.12030 0.00000000 0.0000000 0.000000
## OwnOccMedVal 0.20460 0.00000000 0.0000000 0.000000
## OwnOccHiQuart 0.15785 0.00000000 0.0000000 0.000000
## RentLowQ 0.20174 0.00000000 0.0000000 1.000000
## RentMedian 0.10260 0.00000000 0.0000000 0.000000
## RentHighQ 0.12826 1.00000000 0.0000000 0.000000
## MedRent 0.11401 0.00000000 0.0000000 0.000000
## MedRentPctHousInc 0.46039 0.00000000 0.0000000 1.000000
## MedOwnCostPctInc 0.13339 0.00000000 0.0000000 0.000000
## MedOwnCostPctIncNoMtg 0.13480 0.00000000 0.0000000 0.000000
## NumInShelters 0.95746 1.00000000 1.0000000 1.000000
## NumStreet 0.08855 0.00000000 0.0000000 0.000000
## PctForeignBorn 0.50137 0.00000000 0.0000000 1.000000
## PctBornSameState 0.24769 1.00000000 0.0000000 1.000000
## PctSameHouse85 0.13375 0.00000000 0.0000000 0.000000
## PctSameCity85 0.12579 0.00000000 0.0000000 0.000000
## PctSameState85 0.22548 0.00000000 0.0000000 1.000000
## LandArea 0.17502 0.00000000 0.0000000 0.000000
## PopDens 0.12907 1.00000000 0.0000000 0.000000
## PctUsePubTrans 0.13151 0.00000000 0.0000000 0.000000
## LemasPctOfficDrugUn 0.08584 0.00000000 0.0000000 0.000000
## agePct22t29 0.24852 0.00000000 0.0000000 0.000000
## BF NA 0.00119545 0.5664238 0.067863
## PostProbs NA 0.00040000 0.0003000 0.000300
## R2 NA 0.27700000 0.2757000 0.278100
## dim NA 16.00000000 13.0000000 15.000000
## logmarg NA 262.09284398 268.2536638 266.131812
## model 4 model 5
## Intercept 1.00000000 1.0000
## population 1.00000000 0.0000
## householdsize 0.00000000 0.0000
## racepctblack 0.00000000 1.0000
## racePctWhite 0.00000000 1.0000
## racePctAsian 1.00000000 0.0000
## racePctHisp 0.00000000 0.0000
## agePct12t29 0.00000000 0.0000
## agePct65up 0.00000000 1.0000
## numbUrban 1.00000000 0.0000
## pctUrban 0.00000000 1.0000
## medIncome 0.00000000 0.0000
## pctWWage 0.00000000 1.0000
## pctWFarmSelf 0.00000000 0.0000
## pctWInvInc 1.00000000 0.0000
## pctWSocSec 0.00000000 0.0000
## pctWPubAsst 1.00000000 1.0000
## pctWRetire 0.00000000 0.0000
## medFamInc 0.00000000 0.0000
## whitePerCap 0.00000000 0.0000
## blackPerCap 0.00000000 0.0000
## indianPerCap 0.00000000 0.0000
## AsianPerCap 0.00000000 0.0000
## OtherPerCap 0.00000000 0.0000
## HispPerCap 0.00000000 0.0000
## NumUnderPov 0.00000000 0.0000
## PctPopUnderPov 0.00000000 0.0000
## PctLess9thGrade 1.00000000 1.0000
## PctBSorMore 0.00000000 0.0000
## PctUnemployed 1.00000000 0.0000
## PctEmploy 0.00000000 0.0000
## PctEmplManu 0.00000000 1.0000
## PctEmplProfServ 0.00000000 0.0000
## PctOccupMgmtProf 1.00000000 0.0000
## MalePctNevMarr 0.00000000 0.0000
## TotalPctDiv 1.00000000 1.0000
## PersPerFam 0.00000000 0.0000
## PctFam2Par 0.00000000 0.0000
## PctWorkMom 0.00000000 0.0000
## PctKidsBornNeverMar 0.00000000 0.0000
## NumImmig 0.00000000 1.0000
## PctImmigRecent 0.00000000 0.0000
## PctRecentImmig 0.00000000 0.0000
## PctSpeakEnglOnly 0.00000000 0.0000
## PctNotSpeakEnglWell 0.00000000 0.0000
## PctLargHouseFam 1.00000000 0.0000
## PersPerOccupHous 0.00000000 0.0000
## PersPerOwnOccHous 0.00000000 0.0000
## PersPerRentOccHous 0.00000000 0.0000
## PctPersOwnOccup 0.00000000 0.0000
## PctPersDenseHous 0.00000000 0.0000
## PctHousLess3BR 0.00000000 0.0000
## MedNumBR 0.00000000 0.0000
## HousVacant 0.00000000 0.0000
## PctHousOccup 0.00000000 0.0000
## PctHousOwnOcc 0.00000000 0.0000
## PctVacantBoarded 1.00000000 1.0000
## PctVacMore6Mos 0.00000000 0.0000
## MedYrHousBuilt 1.00000000 0.0000
## PctHousNoPhone 0.00000000 0.0000
## PctWOFullPlumb 0.00000000 0.0000
## OwnOccLowQuart 0.00000000 0.0000
## OwnOccMedVal 0.00000000 0.0000
## OwnOccHiQuart 0.00000000 0.0000
## RentLowQ 0.00000000 1.0000
## RentMedian 1.00000000 0.0000
## RentHighQ 0.00000000 0.0000
## MedRent 0.00000000 0.0000
## MedRentPctHousInc 0.00000000 1.0000
## MedOwnCostPctInc 0.00000000 0.0000
## MedOwnCostPctIncNoMtg 0.00000000 1.0000
## NumInShelters 1.00000000 1.0000
## NumStreet 0.00000000 0.0000
## PctForeignBorn 0.00000000 1.0000
## PctBornSameState 0.00000000 0.0000
## PctSameHouse85 0.00000000 0.0000
## PctSameCity85 0.00000000 0.0000
## PctSameState85 0.00000000 0.0000
## LandArea 0.00000000 0.0000
## PopDens 0.00000000 0.0000
## PctUsePubTrans 0.00000000 0.0000
## LemasPctOfficDrugUn 0.00000000 0.0000
## agePct22t29 0.00000000 0.0000
## BF 0.03599546 1.0000
## PostProbs 0.00030000 0.0003
## R2 0.27760000 0.2841
## dim 15.00000000 17.0000
## logmarg 265.49771396 268.8221top 5 model
10.3 Visualization of the Model Space
image(fit.gprior, rotate=F)
10.4 Posterior Distributions of Coefficients
coef.gprior = coef(fit.gprior)
coef.gprior##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 31641 models
## post mean post SD post p(B != 0)
## Intercept 32.040573 0.773408 1.000000
## population 2.143175 3.186054 0.404240
## householdsize 0.076734 0.712860 0.110630
## racepctblack -1.573752 3.092283 0.308000
## racePctWhite -2.135769 3.531886 0.385240
## racePctAsian 0.254106 0.844966 0.163850
## racePctHisp 0.541173 1.551077 0.192650
## agePct12t29 0.176217 1.083324 0.144440
## agePct65up -0.194398 1.228221 0.120090
## numbUrban -1.400553 1.989512 0.485690
## pctUrban -1.323449 1.859229 0.459960
## medIncome 0.376474 2.008206 0.128390
## pctWWage -0.836679 2.331470 0.216670
## pctWFarmSelf 0.008667 0.302906 0.093400
## pctWInvInc 1.167247 2.260643 0.294420
## pctWSocSec -0.264674 1.461475 0.135510
## pctWPubAsst 7.259389 2.470309 0.964970
## pctWRetire 0.020054 0.387573 0.087040
## medFamInc 0.485311 2.313313 0.147520
## whitePerCap -1.359176 2.564734 0.314340
## blackPerCap -0.055486 0.337129 0.106680
## indianPerCap 0.024266 0.229567 0.078770
## AsianPerCap -0.201856 0.582698 0.171880
## OtherPerCap 0.532231 0.886121 0.337600
## HispPerCap 0.008384 0.329801 0.084070
## NumUnderPov -0.150960 2.120112 0.146180
## PctPopUnderPov -1.717400 2.847865 0.357040
## PctLess9thGrade -3.367505 2.775747 0.692710
## PctBSorMore -0.207695 0.993985 0.129900
## PctUnemployed 0.185828 0.817010 0.114840
## PctEmploy -0.170923 0.865615 0.121190
## PctEmplManu 1.013548 1.303923 0.456680
## PctEmplProfServ -0.007511 0.464698 0.095960
## PctOccupMgmtProf -0.308382 1.101401 0.155170
## MalePctNevMarr 0.465209 1.278250 0.199760
## TotalPctDiv 7.236784 1.969124 0.992030
## PersPerFam -0.172712 1.306106 0.110760
## PctFam2Par -0.523553 1.773577 0.160890
## PctWorkMom -0.122904 0.543521 0.127420
## PctKidsBornNeverMar 0.293233 1.083908 0.135330
## NumImmig 4.935297 3.984730 0.684630
## PctImmigRecent -0.032099 0.309089 0.084000
## PctRecentImmig -0.066448 0.880221 0.115770
## PctSpeakEnglOnly 0.261269 1.716693 0.136920
## PctNotSpeakEnglWell 0.443560 1.825018 0.163480
## PctLargHouseFam 0.131478 0.812863 0.110410
## PersPerOccupHous 0.409595 1.696769 0.158670
## PersPerOwnOccHous 0.167416 0.931169 0.118440
## PersPerRentOccHous 0.330763 1.032593 0.159930
## PctPersOwnOccup -0.074182 1.087310 0.104840
## PctPersDenseHous 0.327026 1.279110 0.141530
## PctHousLess3BR -0.485907 1.343148 0.188420
## MedNumBR -0.362093 0.912037 0.206510
## HousVacant 0.070922 0.412078 0.101800
## PctHousOccup -0.039648 0.345067 0.098730
## PctHousOwnOcc 0.031382 0.944784 0.091080
## PctVacantBoarded 9.038685 1.113651 0.999260
## PctVacMore6Mos -0.069940 0.409732 0.112260
## MedYrHousBuilt -0.010239 0.437252 0.108930
## PctHousNoPhone -0.680234 1.543345 0.229860
## PctWOFullPlumb -0.378604 0.842466 0.237070
## OwnOccLowQuart 0.075807 1.828055 0.120300
## OwnOccMedVal 1.213120 4.087233 0.204600
## OwnOccHiQuart -0.854063 3.116338 0.157850
## RentLowQ 0.634005 1.666013 0.201740
## RentMedian 0.052598 1.373276 0.102600
## RentHighQ -0.263229 1.492173 0.128260
## MedRent 0.148903 1.323720 0.114010
## MedRentPctHousInc 1.151072 1.504447 0.460390
## MedOwnCostPctInc -0.130374 0.637545 0.133390
## MedOwnCostPctIncNoMtg 0.134915 0.517961 0.134800
## NumInShelters 3.840262 1.391839 0.957460
## NumStreet 0.015178 0.342480 0.088550
## PctForeignBorn -2.966967 3.653157 0.501370
## PctBornSameState -0.785013 1.790411 0.247690
## PctSameHouse85 -0.203785 0.821113 0.133750
## PctSameCity85 -0.138763 0.662226 0.125790
## PctSameState85 0.613753 1.513568 0.225480
## LandArea 0.260845 0.816557 0.175020
## PopDens -0.144130 0.599277 0.129070
## PctUsePubTrans -0.121727 0.523761 0.131510
## LemasPctOfficDrugUn -0.007959 0.270418 0.085840
## agePct22t29 -0.598228 1.327026 0.24852010.4.1 individual plot
probne0 > 0.2
survivors = which(coef.gprior$probne0 > 0.2)
plot(coef.gprior, subset = survivors, ask = F)
10.4.2 coefficient plot
plot(confint(coef.gprior, parm = survivors))
## NULL10.5 Prediction
muhat.bma <- fitted(fit.gprior, estimator = "BMA")
bma <- predict(fit.gprior, estimator = "BMA", newdata = data)
result_data = original_data %>%
mutate(pred_y=bma$fit)## Warning: Ignoring 91 observations